I have had a similar problem. In my fridge, i found 3 bad electrolictic capacitors in the main board. If you know how to dissolder, it is possible to replace them at low cost.
Get the refrigerator out of the power source and let it discharge. Find the main board casing and open it.
Check for stuffed capacitors. It is probably the ones that powers the relay. Or you can replace the whole board. There are videos on Youtube about it.
chech the door switch,if its o.k. then the center terminal in the bulbs base can get smashed down too far for the lamps center terminal to make contact,power down and carefully lift this center terminal upward,but be careful because its cold and it can break off
It sounds like your motherboard=> WR55X10942 took a hit from a surge. Unplug for a while and replug and see if compressor will come on. If not then unplug and pull away from wall, remove panel covering motherboard and carefull examine both side of motherboard for burn marks and melted solder. If you would like me to give full details of how and what to replace please ask. You model is known for being tricky to repair and asking for assistance would be a good idea if you plan to do this yourself, Thanks Sea Breeze
I have a GSH25JSRFSS GE refrigerator. Twice, the water line has frozen near the dispenser. Each time I used a hairdryer to heat either the side of the door where the water line runs and blew hot air up the dispenser. This last time, I took the plastic cover off the outside of the door (it clips on) and blew hot air into the small holes in the door that the outside grate clips into. This allows the hot air to get inside the door, and I heard ice from the frozen line drop. Subsequently, the water line worked. Two points: I did have water running to the line in the bottom of the refrigerator, so I knew it was an ice clog, and secondly, I took care not to blow hot air on the exposed wires inside the door.GKAZ