Take the top guard off the unit and look for loose wires, that's often the problem. The clicking is probably a relay trying to kick the fan on and since it is clicking, it is likely OK.
See if there is a capacitor on the motor or nearby. If so, disconnect it and use an audible Ohmmeter. Touch the contacts to the two clips on the capaictor; if you get a high whine that decreases to a low whine, the capacitor is OK.
Take the motor off, remove the fan blade and take the motor to a dealer. They can check the motor for you and, if necessary, sell you a new one.
The buzzing you hear may be a Copeland scroll compressor; they make a low humming sound. Without the fan working the compressor will run until the pressure gets too high and then kick out. The fan releives the temperature which lowers the pressure.
As usual, I have talked too much, please let us know how you come out with the fan.