With the small solenoid control wire connected to the solenoid, and all safety interlocks satisfied, have someone turn the key to start while you check for voltage with the volt meter.
If you DO NOT detect battery voltage with the wire connected to the solenoid while key is in the start mode, but you DO detect voltage when the wire is unplugged from the solenoid, that means there is too little current flowing in the circuit to actually operate the solenoid via the OEM starter control circuit.
Explanation for that is: It actually takes a fair amount of current to operate the solenoid, while it takes very little current to operate a volt meter.
The circuit is capable of delivering enough current to register a 12 volt reading on the meter, but not enough current to operate the solenoid.
The test in step 1 will reveal if the circuit has such poor continuity that insufficient current is being delivered to the solenoid by showing that no voltage (or just a trace of voltage) is present if tested with the wire connected, even though it shows voltage on the wire when it is disconnected.
In other words, the solenoid is completely absorbing the paltry amount of current delivered by the circuit, to the point that voltage will not show on the meter.
If this is what you find, there is a defective condition somewhere upstream of the solenoid, could be at the brake switch, PTO switch, or at the ignition switch.
Check for corrosion at all the switch connections that relate to the starter control circuit.
If you can positively identify the wires in each switch so that you know which wires are going to the solenoid..........you could jumper a hot wire to each switch location to determine where the deficit is occurring. But, you gotta be careful you don't touch a hot wire to the magneto kill circuit or it will do exactly that.....it will "kill" the magneto.
Typically on Craftsman the starter control circuits are White wires, and the kill wires are Black wires (which is also ground). You can also jumper the 2 white wires at the brake to determine if that switch is fault without having to use an auxiliary hot wire from somewhere else. But for the ignition switch and the PTO switch, you will need a separate hot source to check (assuming the tractor has an electric PTO).
If it has a manually engaged deck, you can jumper the white wires on that switch just like the brake switch.
Jumpering these switches is a test procedure/method, not a remedy.

This post was edited by mownie on Thu, Jun 12, 14 at 11:58

Thank you so much!!!! Think I have it narrowed down to loss in the female plug that the ignition switch plugs into. Will investigate further tonight to see how to fix it, as when I giggle the wires in the housing, it will crank. Bad thing is that Sears does not sell the female plug. It is only sold with a complete wiring harness ($110).

Hopefully cleaning connections on the female plug will help!

Thanks again for your help!!!! Awesome, Awesome response!!!

The good news is that should you need terminals for that said plug, they are readily available at an OPE dealer. Maybe even Radio SHack? A small like an eyeglass screwdriver will help you to release the tab and slide out the old brass terminals.

Tomplum is spot on there.
I have repaired "worst case" problems (where plastic connector melts or breaks) by replacing the connector assembly with individual, insulated wire spade terminals.
But using the individual terminals means you have to be absolutely certain you understand exactly where each wire is supposed to go.
To release a spade terminal from the connector body, insert a small screwdriver into the business end of the connector (in the direction indicated by red arrow) to depress the locking tab that secures the terminal to a lock notch in the plastic. While holding the locking tab down with the release tool (screwdriver), gently pull on the wire at the back end of the connector. If the release tool is in place properly, and the connector is not melted, the wire and terminal will slip easily out of the connector.
I have also had success with just cleaning and tightening the terminal by ever so slightly closing the gap of the terminal with a small pair of pliers.
Cleaning can be done using a small, stiff sliver of sand paper inserted into the open end of the terminal, but it requires patience.If the terminal has a dark or blackish appearance, don't even try to clean it.....it has been hot and is no good now. Replace it.

Update on this. Still fighting the issue. What I have done..

Replaced all connectors with the one above on both the ignition switch and the PTO switch.

Ran new wires for all black, white, and red wires between ignition/PTO/Solenoid.

Still won't start. I still have 12v at the white wire on the solenoid, but when I connect it to the solenoid, voltage drops to 4v. However, I can run a jumper from the battery to the solenoid, connecting to the same place the white wire connects and the solenoid engages and starts.

You obviously have a high resistance connection somewhere.
How about posting the Sears 917.xxxxxx number?
That may help simplify troubleshooting.

EXAMPLE- IF this tractor has a Voltage Regulator instead of Charging Diode, the headlights work with the engine OFF.
Do they come ON fully?
IF so, what do they do when you turn the key.
IF they don't come on fully when they should, the bad connection is likely in the ignition switch and/or plug.
Also check the condition of the fuse holder.

This post was edited by bill_kapaun on Mon, Oct 20, 14 at 2:41

917.273070

Headlights work. Have replaced the ignition switch and cut the plug out replacing it with the above connectors.

Fuse holder tests clean with no loss.

You still have the brake/clutch switch and its connections.

Yes - I currently have the switch cut out (for testing purposes). Pretty sure the switch is good when it's wired in, as it kills the voltage on the white wire when the clutch is depressed.

I have ran new wires for all black, white, and red wires.

"If I engage the blade, voltage drops to 0 as well, so that switch is good. Same with the seat safety switch, so I assume all switches are functioning properly."

I MISSED the seat switch part.
1. The seat switch has NOTHING to do with cranking.
All it does is complete a circuit to supply 12V to the Operator Presence Relay.
The OPR draws about 1/6 AMP.
Apparently the ignition switch has such poor contact that it can't supply even that.

Try this for a test-
Disconnect the carb solenoid lead and hook the volt meter to it, positioned so that you can easily read it.
It's the same circuit as the OPR.

Do the "start" procedure.
IF the voltage drops to zilch, the problem IS in the key switch or connecting plug.

Do you have a schematic?
IF not, it's in the OM at the link below, page 35/60.

BTW, is the CORRECT ignition switch installed?

EDIT-
Thinking about this some more-
The head lights are on the same circuit as the seat switch.
It wouldn't make sense that they work, but closing the seat switch would drop the voltage to zilch.

Here is a link that might be useful: Link

This post was edited by bill_kapaun on Tue, Oct 21, 14 at 11:19

Is the carb solenoid different than the ignition solenoid?

I have tested the white wire to the ignition solenoid and get 12v with the key turned and the wire disconnected. When it is connected to the solenoid, the voltage drops. Solenoid is good, as I can run a jumper wire from the battery directly to the solenoid post (where the white wire connects) and the engine starts.

Of course the carb solenoid is different from the ignition solenoid.
1, it's connected to the carb.
2. it doesn't draw nearly as much power as the starter solenoid.

It only takes a few milliamps of current to make your meter read 12V.
When you are loading the circuit with a couple (or so) amps, the high resistance isn't allowing enough current to flow to maintain the voltage.

8 penlight batteries will generate 12V. They won't supply enough current to crank the engine however.
Guess what the voltage would read if you tried?
It'd drop to zero or thereabouts.

Have you checked your positive battery cable connector at the battery ? Wondering when you add a jumper if you are improving that connection temporarily ..?