Check the breather hole in the gas tank cap! Little bugs lay eggs in any hole they can find, which eventually stops the flow of fuel from the tank, even ones with a fuel pump! When that happens---no start--no run! Oh, ya might get 30 seconds of trying to run, but its like sucking on a rubber hose, with yer finger over the end!
I had a guy follow me home, to ask me to look at his lawn tractor. When i got there--his symptoms were the same as yours. A bit of poking in the little hole opened it up. And, the tractor ran good again.
Try starting it without the gas cap on the tank opening. Might surprise you!

Rusty, Thanks for the suggestion, but no joy.

Let's concentrate for now on the finding that "one of the valves does not compress as far as the other."
That is significant, especially if you can tell the difference without any measuring intruments.
Valve adjustment is a precisely orchestrated series of steps to get the engine positioned to the right point in the 4 stroke cycle before you can check or adjust the valves.
Now, let's see what we can find out about "why one valve doesn't compress as much as the other".
You need to get the engine to Top Dead Center on the COMPRESSION stroke. Because you have little or no compression you will not be able to sense it by placing a finger over the spark plug hole. Instead you will need to watch the valves and rocker arms as you turn the engine by hand.
Rotate the engine until BOTH rocker arms have no contact with the valve stems.
When you reach this point, take a small pocket ruler and measure the height of each valve spring. Measure from where the bottom of the spring rests on the cylinder head up to the edge of the cup washer on top of the valve spring.
The springs should measure exactly the same for both valves.
If you find one spring appearing shorter than the other, you will also find it is the exhaust valve. This indicates that the valve seat has ejected from the head and is holding the valve open. Head will have to come off to repair this (if this turns out to be the case).
Check the springs length and post back.

Mownie, you nailed it. The intake valve (bottom of engine) comes out considerably more than the exhaust valve (top) of engine.

Thank you for the pointer!

So I gotta pull the head off, eh?

Is it possible to simply remove the head w/o taking about the rocker arms and valve connecting rods?

To get the valve springs back in place do I need a spring compression tool?

E-mail me for a PDF service manual.
Yep, head gotta come off. Rockers could stay in place but it's no big deal to take them off. Briggs manual says take them off, but then there's a photo showing them still on the head as the valve spring retainer is being removed.
Finger tip pressure on the valve spring cap while holding the valve face with the other hand is all that is needed to manage the valve spring.
If you have a digital camera, start taking pictures (you really should have begun doing that) of everything as you remove things (before and after a part is removed) so you create a map of the teardown, it makes it easier to confirm how it goes during reassembly.
Mark or ID the pushrods as to location (aluminum is intake, steel is exhaust).
Click the link below to read a recent, similar case where a valve seat ejected from the head.
Also, beware!!!!!!! Valve seats rarely come loose unless the engine has run hot!!!!!!!
You need to remove the sheet metal cooling shroud from the engine and look for debris (grass, leaves, paper bits, pieces of cloth, etc.) that was packed in by small rodents (aka "mouses").

Here is a link that might be useful: Similar case for ref

Thank you for the pointers. I'll spend some time on this over the weekend. I know it's got a ton of grass stuffed under the engine, guess I need to tidy up a bit...

Celebration day today! 4th of July and the end to a broken down tractor.

Thank you thank you thank you Mownie!

I pull the cylinder head, found the valve seat was indeed out on the exhuast valve. I cleaned the seal and valve a bit, popped the seal back in. Put the thing together, and poof, engine started almost immediately. Even sounds better than it had.

Still have some work to put all the cowling and carb stuff back together but I can finally get this tractor out of the gargage and back to the shed.

I was inches away from rolling the thing to the curb.

Was even able to go back to the rebuilt carb that I have and can try to sell the new carb I bought due to mis-informed troubleshooting.

Saved me many $100's, money I dont' have to spend.

Thank you again mownie.

Great that it's going again, but.......I don't see where you say you "peened" the cylinder head to secure the seat from ejecting again. Did you click the link I furnished a couple of posts above and read the part about peening the cylinder head??? If not, the seat will come loose again. :^(

I peened and peened again. Whether I peened enough remains to be seen.

Thanks again Mownie!

Good for you roz. My definition of a darn good peening is to start peening at the 12 o'clock position, then at 6, then 9 and 3. Keep peening in alternate strikes until the entire perimeter around the valve seat has been struck.
Never peen in a continuous, "serial" movement around the valve seat!! Always use the "criss/cross" technique to tighten the cylinder head's grip on the valve seat.