I'd pull the valve cover and look for anything obvious.

With the spark plug removed, and the spark plug wire away from the area (so it can't touch your hand), put your thumb over the spark plug hole and see if you can feel the compression that is supposed to be present when the engine is cranked with the starter.
If the compression is good it should be difficult or impossible for you to keep your thumb pushed against the hole.
If the engine has little or no compression, you may need to enlist someone to check further as the exhaust valve seat might have come out of the head, or a valve guide could have gotten loose.
The oil on the spark plug (and the heavy smoke) might indicate that the head gasket has blown, and if so.........that is a relatively easy and inexpensive repair.
But.......oil on the plug and smoke can also mean some other problems (like a hole or crack in the piston) and costs accelerate exponentially if that is the case.
I know you guys can post photos so if you get to the point of having something for us to look at, put 'em up.

Thanks for the fast follow-ups!

Not sure whether or not we'll have time to play with the engine tomorrow, but we'll be sure to update you all as we get more information and/or photos.

Nice to see you again, Mownie - Hope your garden's doing well.

Lynda & Pat

Yep, my little garden has been very nice. Thanks for those heirloom seeds you sent. The peppers apparently do not like our soil but those Black Cherry tomatoes sure do. And I like them.
My favorite thing to do when they start coming in is to pick a bunch for my lunchbox before I leave for work.
The end of season in 2011 I canned (pickled) 20 quarts and around 15 pints of green Black Cherry tomatoes one Saturday in October because a frost predicted overnight was going to close the curtain anyhow. Thanks again.

We did the Mownie test, and there was minimal pressure and a light coating of oil.

Pat opened up the valve casing and found these items loose inside. They appear to have broken off the lower valve.

OK, what do we do next? :)

The best advice I can give you at this point is to remove the cylinder head from the engine to inspect for further damages.
I suspect that there is also a bent valve push rod lurking in the push rod gallery and possibly a bent intake valve. Maybe damage to the piston as well.
Unless Pat is pretty savvy on engines, this is best left to a professional mechanic or a close friend with credentials on engines.
It will sort of go like this:
The large round disc in your photo is the intake valve spring retainer cap, and it is damaged beyond re-use. That implies that the valve guide in the head may have loosened and climbed out of its bore, ultimately causing binding and bending of the rocker arm parts and push rod. A photo of the head itself might show the valve guide has risen.
But anyhow, continuing on. The intake valve might have been struck by the piston after the valve got loose from its spring. If the piston has struck the valve and bent the valve, it has probably also damaged the piston. Photos (as good quality as the one above) would be enough for us to offer advice on what to do in that case.
But, the head will have to come off to view what's underneath.
You guys will have to make the decision on whether you want to DIY it or farm it out.

Took off the cylinder head today. Here are some pictures of the damage, hopefully all self-explanatory.

As we have four pieces of equipment with Briggs OHV engines and no convenient way to haul a tractor to a repair shop, learning how to fix this ourselves could be very useful, unless you think this is something that definitely needs a professional to do it.

Thanks.

Here is a link that might be useful: Photos Set showing damaged engine parts

In picture C_Head2
That piece almost looks like the throttle plate out of the carb.

Else, it looks like a new head assembly should do the job.

Bill has made the correct identification of the foreign object (foreign cause it's not where it belongs).
It is in fact the throttle plate from the carburetor throttle shaft.
How about a picture looking down into the throat of the carb now?
I concur with Bill's thoughts that a new head assembly should take care of the damages seen here.
But I am still suspicious of the intake push rod being bent (and I don't see it in the photos.
It will also be best to get a new carb too as I expect the throttle shaft itself has damage (based on the fact that 1 rivet is still showing in the throttle plate).

Photos as requested.

As you can see, one of the rods is noticeably bent when compared with a straight edge. I've forgotten which is which, but I assume that the upper one in the picture is from the exhaust valve. The other one might be very slightly bent too.

It's tough to make out too much peeking into the carb throat, but the choke plate seems to open and close OK.

Thanks for your help with this so far. Anything else we need to do before ordering the parts?

Here is a link that might be useful: More photos

Yes, you need to remove the black elbow adapter from the carb and take pictures looking straight into the carb, from both ends.
Top push rod is the intake rod.Definitely bent. Replace it and make sure it is aluminum just like this one.
The exhaust push rod is made of steel.
Easy way to check push rods for bending is to roll them on a flat surface (table or counter top) and watch how they roll.
Try it with yours and you will see what I mean.

Pictures of the inside of the carb, as requested.

Here is a link that might be useful: Photos

Photos Carb 8 & Carb 5 show perfectly where the throttle plate separated from the throttle shaft.
I would replace the carb with a new one.
Make certain you clean off the top of the piston and inspect it closely for pieces of the 2 screws that once held the throttle plate in place. They probably got chewed up and passed out through the exhaust valve but I have seen them stuck into pistons and inside the head surface too. You don't want to leave any "seeds of destruction" in there.

The top of the piston is dinged up in a couple of places, but we don't see any sign of those screws.

Is this likely to have been due to adjusting the valves and the carb, or was this something that was just waiting to happen anyway? How many of the previous parts can be recycled, or it is best to replace the whole lot - cylinder head, valves, rods, carb, etc.?

Thanks again for all your help with this.

This event had nothing to do with valve adjustment nor carb adjustment.
This entire scenario can be blamed on loosening of the screws that secure (well, supposed to secure) the throttle plate to the throttle shaft.
Those screws are "staked in place" after installation by the OEM builder. If ever those screws are removed in the field for repairs or cleaning of the carb, new screws should be used and those should be staked after tightening. Some folks omit those details. If the screws had ever been taken out of the throttle shaft, I would guess that was the "moment of conception" for the mess you have now.
Your best bet here would be a new or "good used" complete cylinder head.
A new or "good used" carburetor assembly.
A new or "good used" intake (aluminum) push rod.
And a head gasket KIT.
The piston is likely not compromised if you only see a couple of superficial dings. The remnants of the screws have been passed out through the exhaust valve and likely spit out somewhere on your property a short time before you heard the awful racket and saw the covey of dollar bills flying away.
The best way to recycle the old parts is at a metal recycling center.

Thanks - it's reassuring to know that it wasn't our fault.

By "complete cylinder head' you mean with the valves, springs, rockers, etc. - the full works?

Yep, the full Monte, already assembled out of the box and ready to be installed on the engine block without further ado.
But you still have to get the carb, the head gasket set and the intake push rod separately.
And the valves will of course need to be adjusted before you try to run the engine.
:^)

Hi again Mownie -

We're ordering the parts and just want to make sure we're clear on what you mean by "head gasket kit/set".

Is the one in the link what you are describing? (Gasket "set" part# 1095, top of diagram )

Here is a link that might be useful: Part 1095

Yes, that is what I call a head set. Briggs calls it a valve set.

We finally got the parts and the time to do the repair - only took us a month!

Double checked that there were no stray bits of debris and thoroughly cleaned off the old head gasket, etc. Installed the new carb, cylinder assembly and push rod. Double-checked that the rods didn't get mixed up, set the valves to about .004", put on the valve cover with a new gasket and changed the oil.

Nervously turned the key and - nothing!

Checked the battery and it was almost completely flat. Hooked it up to the charger, which said it had an internal shorted cell and refused to charge it. Took it of the tractor and tried again, same result

Went out and got a new battery (340 CCA), checked it was fully charged, hooked it up and even more nervously turned the key. This time the flywheel turned about a quarter turn or so and was followed by a rapid clicking, possibly from the general area of the solenoid. Tried a couple more times with the same result. Flywheel turns OK by hand.

Any suggestions what to check next? And thanks again for past and future help with this.

This post was edited by lgslgs on Wed, May 22, 13 at 22:31

From your description of the rapid (or rabid) clicking it sounds like the new battery was discharged when sold to you. I know you said it was fully charged but if that was based on a volt meter reading, that is not proof of a good battery.
Considering that a battery deteriorates rapidly if left to sit in a discharged state I would return the battery to the place of purchase and have it tested. Wait around while the test is done. If their test results show the battery to be "dead" or discharged, insist on another new battery as this one may actually be defective and not simply discharged.
Have you tried jump starting the tractor with a set of jumper cables to a car or truck? If the engine cranks over when jump starting makes the case for a defective new battery even stronger.
However, if jump starting does not improve the situation you should go through all the battery cables on the tractor, hots and grounds........and loosen and re-tighten them to assure all are making good conductors.

Hooked up another battery - this was 800CCA. It turned it and there was no clicking, but it wasn't even close to spinning it properly. The flywheel just sort of lurched instead of spinning.

Aside from the anti-backfire thing at the bottom of the carb, we shouldn't have touched anything at all to do with the electrical system when we replaced the carb and the cylinder head. Before the old carb spat the throttle plate into the engine, it was starting really easily.

We'll go over the connections anyway.

Will the engine spin with the spark plug removed from the head?
Can you turn the engine by hand with the spark plug out?
If it turns OK with spark plug removed, it may just be that the valves have not been adjusted properly and so....compression is not being released sufficiently to permit cranking, even with a hot battery.

It turns easier with the plug out, but still won't start. The small battery will spin the flywheel a few times before the clicking starts. We'll double check the valves anyway.

OK - this time, tried turning it with the spark plug removed AFTER recharging the battery! Apparently, the few attempts at starting it had almost completely drained it. After the recharge, it turned over really easily. So we went ahead and pulled off the valve cover. Exhaust valve was fine, but intake valve was visibly looser than it should be. Re-set it down to .004" and the engine starts perfectly.

Our concern here is that we had set the valves, then rechecked them later, but today that intake valve was way out of adjustment. Did we simply undertorque the set-screw, or does it need a dab of Loctite?