Have you tried jumping directly across the big posts of the starter solenoid? If you jump across them and still get no response from the starter you probably have an issue with the starter itself.
It is also possible to have power arriving at the starter but the starter be inoperative due to the engine having lost its ground path (via the engine to frame mounting bolts).
You also need to jump a wire (for testing) from the BATTERY cable on the solenoid over to the small solenoid terminal (the one with White wire on it) to see if the solenoid is even working as it should.
If the solenoid activates when you jump to the small terminal, then you have a problem in circuits coming from the safety interlock switches or maybe even the key switch itself.

have jumped directly from battery to starter and do get a response,,,so starter seems fine....have not tried jumping from the battery cable to the white wire on solenoid. willdothat.I'm beginning to think key switch...thanks much

You made sure the attachment switch is OFF?

The schematic is on page 31 of the owners manual.
When the key is in the START position, the S terminal of the key switch get's "hot".
12v travels along the WHITE wire through the clutch/brake switch, then the attachment switch to the small terminal of the starter solenoid.

The carb fuel solenoid should click ON/OFF as you switch the key switch ON/OFF.
IF it isn't clicking, you may have a bad FUSE, key switch or connector to either.

This post was edited by bill_kapaun on Sun, Dec 8, 13 at 17:24

bll, I think you're talking about clutch/brake switch when you say attachment switch.Replaced the 20 amp in line fuse,so it's OK. don't think the fuel solenoid is kickingin. will check, and thanks for all the help

Attachment switch is the safety interlock switch that is used with the DECK engagement mechanism.
It is part of the PTO switch when an electric PTO is used.
When a manually engaged deck is used, the term attachment switch is used.
Basically, the attachment switch prevents the starter from being activated if thew deck is left engaged, so you don't impose all the deck load on the starter in addition to the job of spinning the engine.
Since your deck is manually engaged, attachment switch applies.

mowie...I follow you. whats the purpose of the lockout switch under the solenoid that is activated with the brake/cluth pedal. just jumped from direct12v to white terminal on solenoid and engine turned. but, the fuel solenoid doies not engage with key in the ON position. Thinking about replacing the key switch, and both the lockouts...where's the best place to buy parts online..thanks much

know I'm worrying you all to death..so thanks for your patience with a dumbutt, buthadn't had to work on this mower before, so am learning what does what. just unplugged the connecter on the brake/cluth switch, and with the key in theON position, could not register a reading on the voltmeter from the white wire, which I'm told is the 12v feeder to the deck lockout to the solenoid...makes me think there is a switch key problem...whadda think...thanks

It sounds like the key switch is bad-
HOWEVER- Try unplugging/plugging the connector a couple times to make sure you don't have a bad connection.

IF you need a switch, Google-
AYP 175566 switch

or look at your local dealer.
It's a pretty common switch. Get the CORRECT part#. Not all switches are wired the same internally.

This post was edited by bill_kapaun on Mon, Dec 9, 13 at 15:45

OP - just checking - you or an assistant is sitting on the seat and fully depressing the cl/brake pedal each time you attempt to start the tractor during the above tests?

Seat switch would have nothing to do with the fuel solenoid not getting power or cranking.

Lowellt, The clutch/brake switch is part of the starter interlock safety circuit AND also part of the seat switch safety interlock circuit.
The clutch/brake switch and the attachment switch are both actually 2 switches in a single package.
Each switch assembly has 2 small switches in it.
In each assembly, one switch controls the starter interlock circuit while the other switch controls the seat switch safety interlock duties.
The starter interlock prevents you from activating the starter while the clutch is engaged so the tractor doesn't take off if it's in gear.
The seat switch interlock is to kill the engine if the clutch is engaged, or if the deck is engaged, when the seat is vacant (such as would be the case if you fell off the tractor while mowing).
But I agree with Bill on this, it seems that your key switch may be faulty.

Kapaun - this dumb old retired Simplicity Q.C. Mgr does happen to vaguely recall something about the AFTERFIRE control solenoid getting 12vdc when the ignition sw is turned to on position... but if that seat switch isn't activated by weight in the seat, that starter solenoid isn't gonna get it's needed 12vdc signal to energize and cause that starter to turn over.... and THAT was the point of my question to the Original Poster, not you.

rcbe
Look at the schematic!
Seat switch has NOTHING to do with activating the crank circuit!

Your totally wrong suggestions only serve to confuse the OP.