In addition to the other suggestions, check that the bail arm is functioning correctly and in the down position (iow, bin is not full of ice). If not, the new ice cubes will never eject, and new water will never fill the freezing tray. Check anything else that might tell the ice maker to halt its cycle: door switches, thermostats, bin sensors, etc.
Also, make sure the ice isn't jammed into the freezing tray, which would prevent the ejection fingers from ejecting the cubes.
We had a similar problem with the ice maker in our freezer. I don't remember the fix, but it turned out to be simple. I think the bail arm was not going down far enough due to ice buildup or a lodged cube.
H