Thanks to all those that replied to my original post!
First, the fridge is a "Westinghouse Monaco Frost Free". I've checked for the
starting relay, and I assume it is the small part (in this model anyway)
affixed to the compressor itself. Three small connectors forming a triangle
extrude from the compressor and they insert in (what I identified as) the
relay,holding it into place.
The relay also has a round moving part at the bottom that is held by some kind
of connector. I assume that this part is responsible for starting the
compressor and defines this gizmo as the relay.
Now, I'm not sure if it was malfunctioning but as I tried to pull one of the
wire from the relay, a connector on the moving part was really frail and broke.
So I'm getting a new one and hopefully it will fix the problem (yeah, right!).
I have to wait for that part as the store I went to had to order it. In the
meantime, is there a way to test the compressor itself to see if it's working?
I dare not do anything with the three connectors coming out of the compressor
without some advice first! I have a good meter and basic knowledge of
electricity (enough to know that electricity is a very dangerous friend!).