Too hard to say without knowing more. Is it a frost free model? Who made it? Whati is the model number? It could be something in the defrost system, a thermostat, heater, timer, or something else. Are the symptoms still the same? Is the freezer getting so warm that the food is thawing?

Thank you for responding. It is NOT a frost free model. It is a White Westinghouse freezer. Model # FU100L. I unplugged it and tonight plugged in again, but no sign of cooling. I removed the contents when I noticed it not running and placed them in my refrigerator freezer. I thought tomorrow I would pull it out and look inside of the back. Funny really, because I don't know what I would be looking for, but it seems like something I should do.

I suggest you unplug the freezer, pull it away from the wall so that you have access to the rear of the unit. Remove the access cover. With the unit STILL UNPLUGGED, gently use a duster and vacuum to clean all of the visible coils in the bottom of the machine. Perfection is not necessary, but if the unit is really packed with dust bunnies, get them out of there before continuing.

Next turn the freezer on using the thermostatic control. Then plug in the machine.

Listen for the sound of the compressor motor starting up. It should not be an "electric" sort of sound, it should sound like a motor is turning inside the sealed compressor. If it is not running, it could be one of a few things:
Bad Thermostatic control
Bad Compressor
Bad starter relay

The thermostat is 100 bucks, the compressor is 200 bucks. The labor to replace the latter will be at least 200. But the starter relay is 4 bucks and you can replace that yourself with just hand tools.

There are no guarantees that that will fix it, and you should only replace it if you DO NOT hear the compressor start and run. If the compressor runs but it isn't cooling, then it's the compressor or a refrigerant leak or some other problem in the sealed refrigeration system and likely not worth fixing in a unit of this age.

But, if you do not hear compressor starting, that could mean failed thermostat, failed relay, or, again, a failed internal component on the compressor. The only way to determine for sure which of these components has failed is to use a multimeter. But, for 4 bucks you can eliminate the relay as the cause by replacing it yourself. You might consider trying that if you do not hear the compressor start up.

If you want to try to winnow this down some more, post again today with the results of your investigation, pay attention to sounds, clicks you hear, whether the motor starts, and how dirty the condenser coils are.

Cheers and good luck with your troubleshooting.

I pulled the freezer out from the wall. I vacummed (although it was not very dusty). There are no visable coils. I had it plugged in over night. No cooling. The compressor was very warm. I had to take my fingers off after about 3 seconds. With the thermostat on, I plugged in the freezer. I could hear a faint hum/buzz, but not what I would think would be the motor turning, no other sounds
Hubby says he's concerned about fire risk, and would feel more comfortable with a new one. He'll check out the relay switch. Thank you for your knowledgable response.

You have likely eliminated a bad thermostat.

You can pull the existing relay out and shake it. If it rattles like the insides have come apart or something is loose in there, it is likely the answer to your problem and a cheap/easy fix. Other than that, the problem is likely in the "too-expensive-to-fix" category and you should replace the unit.

Depends on what kind of relay is involved. An old-style compressor start relay is a magnetic coil that does make a rattling noise when shaken, so that's not necessarily an indication of a problem with it.

Do a Google or other search for how to test a refrigerator compressor relay.

If the relay is the problem, it's a cheap/easy fix. Could also be a bad capacitor, if there is one (some units have a capacitor, some don't).

You can look up your model at SearsPartsDirect.com, RepairClinic.com, PartsTap.com, or other online parts sources.

Excellent point, dadoes. I looked for a start cap on the drawings but wasn't having any luck on the pages I was seeing. Good gouge on the relay, also.