If it just stopped working with no warning it is 97% likely a defective capacitor, small can looking device with a couple spade terminals on top, sometimes round, sometimes ovals. Usually 7-15$ at the supply house
There are several problems with your question. First, the compressor doesn't have a fan. Second, you didn't state if your A/C is central or a window unit.
You need to troubleshoot the fan to find out what is bad. Remove the A/C cover to expose the fan motor. Turn the unit on. Does the fan motor hum? If it does, turn the fan in the normal direction of rotation (usually marked on the motor). If the fan starts turning, you have a bad start capacitor. If it doesn't start. he motor is stuck or burned out.
If the motor doesn't hum, the wiring or motor are bad.