If you're working on a GE refrigerator that's dead in the water and you've checked for a good 120vac power supply right up to the J11 connector on the muthaboard, then try this troubleshooting tip from Brother BryanS:
Sometimes a shorted fan motor can give you that same scenario. You can try unplugging j2 fan connector and see if the compressor comes on. If it does then you need to just determine which motor is shorted. I've only this happen to me once and it was the evap motor.
The muthaboard diagram below shows the location of the J2 connector of which Brother BryanS speaks:
You can see a bigger version of the muthaboard diagram here.
If it the refrigerator starts running with the J2 connector unplugged, you should replace BOTH the affected fan motor (usually the evaporator fan) AND the muthaboard. See this topic for a heads-up about getting the correct evaporator fan motor for your model.
To learn more about your refrigerator or to order parts, click here.