Choosing a Replacement A/C Condenser Fan Motor
Recheck your contactor in the compressor cabinet and make sure it's functioning properly and making contact. A buzzing can mean a bad contactor.

Your best bet for a replacement motor is to bring it into an AC parts and supply company or an electric motor supply place. They will match the RPM's, shaft size, rotation, frame size, wiring harness,ETC. Bring the motor with you. In many cases they can test the motor for you. Do yourself a favor and don't try to replace it online. They will tell you it will fit, and believe me, it won't.

You might want to consider replacing the contactor since you'll be shopping for a motor anyway. They're only about $15 bucks