This problem occurs when a solenoid that opens the ice dispenser door fails. I recently replaced it for the second time with a replacement part from Appliance Parts Pros. Our GE Monogram fridge is about 10 years old, so the solenoid lasts about 5 years. It's easy to replace. After turning off power to the fridge, pry off the cover to the dispenser unit, then remove the electronics panel by lifting from the bottom. Disconnect three electrical plugs and place the module aside. Remove four screws holding the dispenser door assembly, set that aside. The solenoid can now be removed and replaced. Tip: I took pictures with my phone along the way to help with reassembly. During reassembly, the solenoid piston has to engage the dispenser door properly. The dispenser unit was moldy, so it was a good opportunity to clean it. Problem solved.