It sounds as if the start windings are weak. Are you sure the new capacitor is good?
Well. you have done the right things.
The confusing issue is if the motor starts with a push it is normally capacitor related.
If stiff and resistant then it is motor.
If the capacitor is indeed good, and you are getting 120v, then the start windings are too weak and the motor must be replaced.
It depends on the failure internally...
here are your choices -
bad bearings.....but those would not allow it to be push started and run easy and once running the motor would get extremely hot. Plus would be a metal noise.
Bad capacitor....same symptoms as you now have, except you already replaced it.
Bad windings....depends on if the condition of the wings as to what heat and rotation is attempted.
less than 120v would result in heat and motor soinning at reduced rate.
The rythem noise could be housing , squirrel cage etc, and the motor would be bench tested for that.
you can remove the motor and take it to any motor repair shop and they test it for free.
I sure appreciate your help in this matter. I know someone that might benefit from this type of service. How did you get into this? Have a great day! Thanks again.
all they have to do is apply to the site and verify 2 years experience. Not a bad hobby.