Hi I have been working on a John deere 111 recently, and got it start.
If you want a look at all the parts you can go to
http://jdpc.deere.com/jdpc/servlet/c...ageServlet_Alt type in 111 as the model and click the plus sign next to "1699 - 108, 111, 111H and 112L Lawn Tractors (with 30-Inch & 38-Inch Mower Deck) - 01Oct04 "
then from what drops down, you select what you want, i usually went with the sectional index because it worked for me, and then select what part you want (careful, they have 3 or 4 lawn mowers here, all similar except for a few little pieces so watch if it says 111).
Also you can go to biggs and straton for some info on the engine
http://www.briggsandstratton.com/mai...nav3&subMenu=3
This requires the engine model (its on the ver front of the engine). They have some stuff, pretty much the same as Jd, it is just a matter of what helps you more.
I would have to say it is possible that the seat and pto switches can be causing a the safey/kill switch to be on. That is just my thought though. I believe you can take the top cover off the engine off and get to the magneto and disconect the kill wire to it, and leave that off to the side (make sure it is not grounded), and I think that would tell you if it is bad or not.
I would advise to be careful doing this since it is an engine and I'm sure you know all this, but please be careful.
I do think the igntion switch and pto switch are wired together, as a safety.
If it is now of the wires to the magneto, then I believe it would have to be the magneto.
This is only what I learned from researching how to get my 111 going (which I am still working on - but it wasn't started in the last 5+ years and no ignition switch anymore).
If can also be a bad ground, if it is looking like anything what I'm working on, there is rust, and the seat switch is grounded to the fender in the back on mine, so I think that could be a weak link.
Sorry to go on, I would suggest by placing all the safety stuff to test it, see if that works. If it does then it is time to look for whre the wiring is bad.
Sorry if there is an easier way, I'm completely off here, as I said, this is just what I learned working on the one I have