Wiggling the wire harnass doesn't seem to affect it. I can set the motor spinning properly with my hand (no humming) but it won't start up by itself, just hums and eventually smells like burning.
The capacitor is used to help start the motor, could be a bad capacitor yet even if it looks good.
How about the connection on the wire harness that plugs into the capacitor are they clean looking?
Could you remove the capacitor and take it to a shop that could test it for you?
The capacitor should say on the side of it the range it should test in for it to be good.