The best fix is to install a new socket in the light kit if it has burned out.
Ceiling fan not working but light is.
Remove the screws holding the switch cover plate over the ceiling fan and.
Replace the batteries in the remote control and turn the power back on.
Turn the ceiling fan off.
Remove the batteries from the remote control and wait for about 10 seconds.
Checking this part of the fan is also relatively simple.
If your ceiling fan quit working but the light still works and you hear a humming sound you might be looking at a blown motor capacitor.
Turn off the breaker supplying electricity to the ceiling fan at you main electrical panel if the tester does not light.
They can burn out for a number of reasons the major two reasons being old age or overheating.