Refrigerator does not cool....?

With that unit that has a single defrost heater it is most likely the heater is bad.

GE is using a heater in a glass tube these days. If, after defrosting, you look at it carefully (you may have to remove the two sheet metal screws that mount it on to see under the cover), you will likely see that the glass tube is black in one place or the whole tube. That means it is burnt out.

The heater is the unit that hangs just under the bottom of the evaporator.

There is a bimetal, defrost terminator, at the top stuck on the coils, to prevent overheating, that can go bad too. It is wired in series. Those fail sometimes.

But with the single heater it is the heater more times than not. The bimetal has to be very cold to close if you ohm it to check.

GE sells the heater, wiring, and bimetal as one assembly. It has a rubber plug on the end where it connects. Once in there, it is an easy replacement. Two screws, route the wiring and plug it in.

On rare occasion I have had a motherboard that controls the defrost fail to defrost but that, as said, is rare.

And with that model you can not trigger a defrost. The only way to test is to jumper it but I won't try to tell you to do that. Most common, you will see that the heater is burnt.

Good Luck.