Hi,
One day I turned on the a/c, noticed my house is not cooling down, and found out that the fan is not on. I can hear the motor and the compressor running. I have the capacitor replaced but the fan still won't come on. Could anyone tell me what is wrong with my a/c? Thanks you !

Are you talking about the fan on the outdoor unit? Does the motor feel free if you turn it by hand?

Yes, it's the outside unit. The fan does move freely.

Are you sure the capacitor is hooked up right? Are the wires all connected for the motor? It may be shorted windings in the motor.

Actually, the fan does come on for about 5 minutes and the house starts to cool down. After the 5 minutes the fan stops and the compressor keeps going for a few more minutes making a humming sound. If I turn to unit off and wait about 30 minutes to turn it back on, the fan comes on again.

After reading posting from people with the similar problem, here is what I have done.
1- changed the capacitor. It is connected exactly like the old capacitor. With the new capacitor the problem has not changed and is the same as with the old capacitor.

Result, fan comes on for 5 minutes and turns off. My feeling is now I may need to change the fan motor. I head that there is a sensor on the fan motor that gets HOT and turns off after only a few minutes. Can that be the problem?
Any ideas if I am in the correct path or if I need to look at anything else?

Thanks everybody for the help!

You may have a bad fan motor they have built in overloads that shut them off. Does the motor sound different bad bearings etc.?