Open the freezer door. You should hear the fan motor running. If not, you will have to remove the rear panel, and check the motor. If it is bad. Replace.
If the fan motor is O.K. then it is a defrost system problem.
1. In the food compartment, behind the main controls is a slot that allows you to advance the timer. With the machine on, turn the shaft of the timer with a screw driver, until the machine shuts off. It is now in the defrost mode. Leave it like that for a minimum of 45 minutes. If it turns the machine back on, it is O.K. If not replace.
2. If the timer checks O.K. you will have to check the other 2 parts. To access them you have to remove the rear panel. One of the items is a defrost thermostat clipped to the top of the coil. To test, the machine must be at temperature. You will need to do theses tests with an ohm meter. The thermostat should test at zero ohms. If not (and it is the item that fails the most), replace it.
It looks something like this.
The last item is the main heater, that runs along the bottom of the coil.
It is a quartz glass heater. It should test out at no more than 35 ohms.
If bad. replace.
Unique to G.E. products, if the problem has been around a lot, the ice and frost buildup can migrate to the air return chutes. You can't see the buildup, nor melt it out. If the repair is done properly, and the machine, unfortunately must be emptied, unplugged, and left off for a minimum of 12 hours.
Here is a neat tutorial on defrost systems.