Test the compressor
Your compressor is going to look something like this
To test the windings, you'll first have to remove the "box" where the wires connect.
WARNING: There's likely a capacitor in here. Take care not to let the capacitor discharge into you.
Once you've go that out of the way, you should see three pins/terminals. They'll typically be arranged in a triangular pattern.
One terminal will be start, one will be run, and the other will be common. To determine if the windings are still good, you'll simply test the resistance between each terminal.
- Set your multimeter to read ohms.
- Touch one probe to each of the bottom pins.
- Write down the reading.
- Touch one probe to the lower left pin, and the other to the upper pin.
- Write down the reading.
- Touch one probe to the lower right pin, and the other to the upper pin.
- Write down the reading.
NOTE: Your readings may vary.
You should end up with something like this.
This tells me that the top pin is common, the lower left is start, and the lower right is run. It also tells me the compressor is still good. The reading from start, to run should always be the largest reading. The readings between start and common, and run and common should total up to the reading from start to run.
If the values are way off, or you get infinite resistance between the pins, replace the compressor.
If the compressor checks out, you'll want to make sure it's getting power.
Check the power to the compressor
After reassembling the compressor, plug the refrigerator back in. Set the refrigerator to a setting that should cause the compressor to come on. Using a multimeter set to volts AC (VAC), carefully probe the two wires connected to the compressor. You should measure ~120 volts.
If you get the proper reading, you'll likely have to replace the relay and/or capacitor. If you don't get ~120 V, the problem is in the control circuitry.
Mechanical failure
If everything checks out, there's still the possibility that the compressor is seized. In which case, you'll have to replace the compressor.
Sounds like you're low on refrigerant. The sealed loop internal pressure has dropped low enough that all the evaporation is happening in the top two layers of the evaporator coil.
You could replace the refrigerant, but the question will remain: what caused the loss? I suggest that a qualified ($$, I know) repairman is your best chance at finding and repairing the leak.
Best Answer
We had a similar odd sound from the back of our refrigerator.
There's a few different parts back there that can make noise: The compressor, condenser fans, and defrost timer. Apparently the fans can be cleaned fairly easily, and the timer can be replaced if its electric motor starts making noise.
In my case, we called in an independent service technician (found via Service Magic). He diagnosed the problem for us at no charge. Unfortunately for us it was the compressor, and a new unit would cost almost as much as a new fridge, so we ended up getting a new fridge.
But in your case, maybe you're lucky and it's one of the other parts.