To find out which wire goes to the battery, use a continuity test. With the battery disconnected, and the key in the off position. Using a multi meter, set to ohms, run a jumper from the positive battery terminal, of the disconnected battery. Hook the jumper wire to one end of the meter, then probe all the terminals on the switch with the other. When you get a reading, there shouldn't be much difference between this reading, and just touching the meter terminals together. There'll probably be some difference, but not much. Then turn the key on, and find the next wire, that'll be the one that's always hot when running. Then the start wire is last. That should just about cover most of the wires on the switch, so you can track down the problem.
But from what I've read so far, it seems like a ground wire problem. But if you can't get continuity at the switch then it's obviously a problem on the positive circuit.