The ice maker in my GE refrigerator will not dispense ice. I've replaced the motor. That wasn't the problem.
Answers:
If the motor isn't turning at all it most likely is the door switch or wiring /connections going to the motor. Seems like you are inclined to work on stuff yourself so I will give you some advice.
On the back or near the compressor there should be an electrical diagram that you can trace the wiring out. take special note of any switches that could interrupt the power going to the motor then find them and ohm them out. Most manufactures have a door switch that if not made (closed then the door is closed) will not allow the motor to turn.
The other option is to remove all of the food and bring the Refrigerator and Freezer both up to room temp. this will allow everything to thaw. you might have some ice causing the problem. Keep both doors open and a fan placed in front will speed the process up.
Other answers:
Check that the tube coming into the ice maker hasn't become clogged with ice. It's on the back wall inside the freezer directly above the unit.
Check that the tube coming into the ice maker hasn't become clogged with ice. It's on the back wall inside the freezer directly above the unit.