When the motor fails on a central AC unit, the fan won't move and no air will come from the vents. There are other issues that can lead to this issue, so you must test the AC to see if it really is the motor that has failed.
Step 1: Power Check
Always start troubleshooting by checking the power. If you have access to a multimeter, you can also check the thermostat to ensure it is getting power. If not, the wiring needs to be checked or the thermostat needs to be replaced. Another power issue is in the breaker box. Circuits do sometimes get tripped in the breaker box. To check, flip the circuit that controls the AC all the way to the off position. Wait 30 seconds then turn it back on. If the AC fan now works, the issue was no more than a tripped circuit.
Step 2: Filter Change
Many air conditioner units have a safety switch that powers them off in the event there is insufficient airflow into the system. A clogged filter or filter housing is the most likely culprit of reduced air flower. Changing the filter and dusting out the filter housing will solve the issue if lack of airflow has lead to an emergency shutdown of the motor.
Step 3: Fan Cleaning
A dirty flan can quickly become clogged to the point it no longer works properly. When this happens, you may be able to hear a hum from the motor in the exterior unit, but the fan won't turn. In some cases, the motor may overheat and shutdown. Disconnect the AC and remove the exterior housing on the unit. Hose down the fan and remove any debris that is entangled in the blades or fan shaft. Often this will fix the problem.
Step 4: Spin Jumpstart
If the motor still won't power the fan, then try to give it a jumpstart. This will only work if the motor is obviously powering on and humming, but the fan isn't spinning. Use a long wooden stake or similar to gently push the fan blade. Do not use your hand, as this can lead to a major injury. If the fan begins to move on its own after a push, then the issue is likely not the motor.
Step 5: Capacitor Test
When a fan will spin with a bit of a jumpstart, the likely culprit is the capacitor. You must still check the capacitor, though, as in some instances the motor could be weakened for some other reason. You can use a handheld capacitor tester to check to see if the capacitor requires replacement.
If none of the above steps solves the issue, then the problem is likely with the fan motor. Contact an AC repair service for further assistance.