That would probably be one of those I was talking about that have the very common ADC board failure. I don't remember the exact model numbers off hand, but I bet it is. If the temperature controls for the refrigerator and freezer are two big slide levers at the very top of the refrigerator section, it will have that ADC board. It may also be a defrost thermostat failure, but thats a 1 in 20 chance. Defrost heaters almost never go out on that refrigerator because it uses the calrod heater.
Heres how to check the ADC board. Please keep in mind this only applies if your refrigerator had the two slide levers for the temperature adjustment. If you kave knobs or dials its a different refrigerator.
Leave it plugged and with the refrigerator running the whole time for this. You will also need to remove the evaporator cover inside the freezer so you can see the frosted up evaporator. Do that first.
Clear everything from the top shelf of the refrigerator and in the back of that cover that hangs off the celing of the refrigerator there will be a finger hole on each side. Stick your fingers in there and with slight downward pressure pull the cover forward. It will slide forward an inch and drop down. Then you will see two 1/4" screws holding the scale (what the temperature settings are printed on, right behind the temp adjustment levers) in to the top of the refrigerator. Remove those, and there will also be another 1/4" screw kind of in the back of that control assembly going in to the back wall of the refrigerator. Its usually painted white so it can be hard to spot.
Then right behind each light there is a phillips screw going in to the top of the refrigerator. Remove those, and then that whole control assemby will be lose and should drop down.
There is a thermostat probe and a wiring harness going in to the left wall of the refrigerator so you won't be able to drop the left side down, just drop the right side down and let it rest on the top shelf. You only need to get in the right side anyways.
Now once you have that control asembly down on the back right corner you will see the ADC board. Its a small control board about the side of a pack of cigarettes. You may need to remove the two 1/4" screws holding the board in from the bottom to test it. Also if the board is encased in a white plastic box you will have to remove the board and snap the box open. Be sure to leave everything plugged in and the refrigerator should still be running at this point too.
Now if you look at that board, where the wiring plugs in there is two terminals (I believe its the 2 on the very left) numberes "TEST" and "L1". You need to jump those together to test the ADC board. A screwdriver works great there, just stick it between the two pins on the back side of that plug where they bend down to go in to the board. Don't short anything or jump anything else together, just the TEST and L1 terminals.
If the refrigerator does not shut off as soon as you jump them, you have a bad ADC board, Replace it.
If it does shut off it just went in to the defrost cycle. Now you need to look inside the freezer with the evaporator cover removed so you can see if the defrost heater is heating. If its real iced up you may have to wait 5 to 10 minutes or so. If it does heat and the refrigerator defrosts itself, you have a bad ADC board. Replace it. If it doesn't defrost but the refrigerator did turn off, it might be a bad defrost thermostat. Use an ohm meter to check it. When its below 40* it should have a closed circuit. Above 40* and it should be open.
If you do get a new ADC board, it will be encased in a plastic box. You may find teh box will not be able to screw in place like the original board did. Thats OK, just set it up in there and put the control assembly back in place. And when you do put that control assemble up, be sure the wiring and thermostat probe on the left side are in the hole in the wall like they are supposed to be. It won't work right otherwise. There is also a foam gasket around the damper hole, be sure thats squeezxed up against the walltight enoufgh to keep too much air from leaking.