It is actually quite common that the GE freezer continues to operate properly while the fridge portion stops cooling enough to keep the food cold. However, there are a number of reasons that can be the root cause so you’ll want to check them all.
Evaporator Fan Motor Dead
One common cause of the warm and cold freezer is the failure of the evaporator fan motor. The fan draws air over the evaporator coils and circulates them through the freezer and refrigerator. If the fan fails then the freezer might seem cold enough but the refrigerator is warm. To check it, see if you can hear the fan moving at any time. If not then there might be an issue.
Damper Control Assembly
It is also possible that the damper control might be stuck closed or broken. The air damper control is essentially a small door that opens and closes to let more or less cold air into the refrigerator compartment. A good amount of cold air needs to flow into the refrigerator as the door is open. It is possible that the evaporator door is frosted closed and now allowing enough air. Try cleaning it out and ensuring that air is getting into the refrigerator.
Temperature Control Board
If the refrigerator is warm but the freezer is cold then it could be an issue with the temperature control board. This temperature control board determines when the fan motors and compressor power on and off. If those components are not working then the temperature control board might need to be replaced.
Main Control Board
GE refrigerators are notorious for main control boards going bad. You can tell just by the number of them that are sold (and reviewed) on amazon. Granted, if the main control board is bad then generally neither the freezer or the refrigerator are cooling but this is always something that should be checked if none of the other items are bad.