If it would quit all together, it'd probably be easier to diagnose:-) What engine does it have? (Model & type/spec) I'm kind of grasping at straws here but- IF you refill the fuel, does it make a difference? IF it's a Kohler engine, did you use the correct Kohler fuel filter? You might "throw" a new spark plug(s) on it.

OH NO! You can e-mail me for a PDF manual covering tests and adjustments to the PTO clutch, though it might be too late unless there is enough of the wiring left intact on the PTO clutch for you to repair and reuse (or at least...repair and test). Your symptoms sound like the PTO clutch might have a break in the wiring inside. This could be causing the the increased voltage that you note on the volt meter when the blades stopped spinning after you engaged the PTO. It would be normal for the voltage to drop in the PTO circuit when current was flowing all the way through the PTO coil wiring (because the wiring is carrying an electrical "load"), then when the supposed break in the wiring opened and no longer carried any current, the voltage would jump to a higher level on your volt meter (because the electrical load is gone now). The fact that the PTO stops spinning the blades but you still show voltage in the PTO circuit says your PTO switch is good and the PTO clutch is bad.

The seat switch isn't in the crank circuit, so you don't have to worry about being in the seat for the SOLENOID tests. Basically, jumping 12V to the SMALL solenoid terminal should result in the solenoid engaging and the starter motor cranking. You are bypassing ALL switches (in the crank circuit) when you do this. Clicking indicates a couple different possibilities- 1. Battery low- As soon as the starter motor engages, it pulls down the voltage enough that the solenoid "drops out". Since the starter isn't trying to turn any more, voltage jumps back up and the solenoid re-engages. Repeat with a "machine gun effect" of rapid clicking. I'd really suggest getting the battery charged and LOAD tested. Autozone and similar places will do a free load test in hopes of selling you a battery. 2. BAD connection in the crank circuit. This is basically your "heavy gauge" battery cables & connections + the ground circuit, which includes engine mounting bolts being tight etc. 3. Possibly a bad solenoid? With your volt meter hooked across the 2 large solenoid studs (it'll read 12V), jump 12V to the small solenoid terminal. IF the solenoid is switching internally like it should, the Volt meter should drop to near ZERO. This is because the voltage is traveling through the "switch". IF the solenoid CLICKS, but does not crank, observe the Volt Meter. IF it shows 12V, it means the internal switch is bad and the voltage is trying to travel through the meter.

It MAY be the little relay that is clipped up by the tower. Does it work with the mow in reverse switched on? The actual model number from below the seat could be helpful.