Brother PDuff enlightens us with this nifty tip for making a quick check of the sealed system (refrigerant and compressor) using your fingers and earballs:

Quick way to check evaporator: With compressor running drain the water from the reservoir by removing bottom cap. Let run for a couple of minutes and check for slight frost on evaporator plate, touch top of plate with wet finger-should stick. If not cold, turn unit off and listen for a hissing noise from evaporator. Not cold and hissing-bad evap. Would replace compressor as well for moisture contamination.

Service manual for this unit is here: http://appliantology.org/files/file/236-whirlpool-15-inch-automatic-ice-maker/

Source: zdis15cssj GE Monogram under counter ICE MAKER not producing ice: