** it makes an audible clicking sound and the ice 'pushers' don't appear to push the ice cubes out of the tray. Or maybe the heater element is broken. **
On the most common icemakers used there is a 'mold heater' that needs to warm the ice mold before it will release the cubes from it. If it was not working the 'rake' would not be able to move the cubes and the gear on the end of it might get stripped (which may be the clicking sound you hear).
In this case if the heater is open, the mold heater or the mold itself may need to be replaced along with the rake if it was damaged. The heater failing to function could also be caused by a thermostat inside the icemaker. I can't think of anything external to the icemaker that would cause such an occurrence.