Hello!
Without being there, it would be impossible to positively diagnosis your unit, but hopefully these suggestions will help.
1.) If you can push start your motor and it runs (probably at a little less than 100% RPM) and slowly overheats/stops, then the most likely cause of the problem is the capacitor. I'd recommend to start by replacing your capacitor.
2.) The motor's start windings could also be going bad, in which case you'd have to replace the motor- but, as mentioned, I'd start with the capacitor
3.) The fact that the motor runs outside of the unit does not really correlate to anything, in my experience, and is something that I'd be surprised if remained consistent. You could check your condenser coil to see if it's completely stopped up and not allowing air flow through it (which should be the only difference with the motor when it is installed), but that would not be consistent with your description of push starting the motor.
I'm fairly confident your looking at a bad capacitor and/or motor. If you'd like help finding the right one, shoot us the model number of your RUUD unit and I can post a link to the proper replacement!
Best of luck!