[BPWilliams]

OK let's see... Battery plus goes to big lug on starter, and key wire goes to solenoid, engine is grounded to frame, negative from battery goes to frame. Turn key moves solenoid into flywheel and starts motor turning on starter. I am not sure if you have a starter solenoid that is mounted somewhere besides on the starter.....? Have you tried to short out the starter with a remote starter switch? It could also have a flat spot on the armature of the starter itself.
I hope that helps,

Brian