Rick,
2 things can generally cause this:
1. The starting capacitor goes bad.
2. A lot of motors have a centrifugal switch. When the motor isn't turning, the starting capacitor is put in the circuit. Once power is applied and the motor gets up to speed, the starting capacitor is removed from the circuit.
What I have seen happen is sawdust gets into the centrifugal switch and prevents the contacts from closing properly. Thus the starting capacitor is never properly put in the circuit.
I have fixed this 2nd problem by removing the end cover of the motor and blowing it out with my air compressor air.