Purchase new bathroom fan (not a big project guy but this seems pretty straight forward). Hooked up wires, white to white, black to black and green to green. Connected power and turned on fan. It just hums, fan does not spin. I have tried to manually spin fan (spins freely), but does not on its own with power.
Verify with a voltmeter that the fan is indeed getting 120V AC. If it does, and there's no physical obstruction to the fan blades, bring it back to where you bought it, the motor is faulty.
If there's no 120V, you'll need to check your wiring, and the switch. Any kind of automatic fan switch (humidity sensor, timer, etc.) is especially suspect. Replace it with a normal on/off switch and see if that solves the issue.