If your tractor battery goes dead over time, try checking your alternator, because it might be bad. If the battery goes dead while driving, your alternator's toast. Also try running the tractor and getting an Volt reader on the alternator wires, which come out of the top of the engine.
You said there was a black wire near the engine that was disconnected, right? That might be your coil wire; I would check if there's a thin black wire attached to the coil, you're good. If there isn't, that might be a problem. When my coil wire was disconnected, the engine wouldn't start or shut off.