If you unplugged and it was working fine, then plugged it back in and it didn't do anything I wouldn't think overheat but thats just a thought.

Starters on engines do the same thing. You will get a spot on the motor where the brushes do not contact very well and you'll get a dead spot. When you tap on it the brushes will make contact and it will go again. We have to hit caterpillar starters from time to time. If they happen to stop on that spot they do it again.

Can you turn the motor by hand with it unplugged? Might be the first place I would start...see if you can turn it.

Maybe capacitor?? I've heard of them blowing...without the capacitor the motor won't be able to start and it will hum. The capacitor holds a good bit of juice for start up. When the motor trys to start, the capacitor unloads all that juice so the motor can start, then it begins running at normal amperage. Kind of like when you A/C in your house kicks on or your dryer and the lights dim for a second.