Stubbyie has some great ideas. I'll pile on.
>11.7 volts is a dead battery. It might be bad enough to not close relays, etc. to run or light anything. A jumper cable to an open circuit battery usually fails to supply enough amps to start the vehicle.
>Just measure the battery dimensions and go to Costco, WalMart, Sam's Club and get a battery of the same physical size. Check the posts to make sure they are in the correct position. Lots of CCA are nice but not that necessary for a tractor that size. Plus, they cost more.
>Get a longer battery ground cable and ground the battery to a bolt on the engine block.
Bet a new battery solves the problem.
EDIT: One more test but it has to be done with care. Instead of attaching the jumper cables to the battery, disconnect the battery ground. Then attach the positive jumper to the positive battery cable and the ground jumper to the engine block. That should bypass the battery and the tractor should start.
If it still won't start then touch the positive jumper to the positive post on the starter. There will be sparks but the engine should crank (the ignition switch and battery are bypassed).