The motor didn't seem to be turning at all to start with. If you give it a kick-start by manually turning the shaft, does it start running? That's a symptom of a bad phase I saw on one of the bots over here. It could be an internal short, which accounts for it warming up so fast. one other thing to look for is wear around where the wires enter the motor case. You might find the insulation has moved or worn through, or that some of the wires have gotten metal fatigue and snapped. That would be hard to fix but its worth knowing why the motor broke so you can avoid it in the future.

I'm with the other guys; its time for a replacement motor.