I would start by replacing the the start relay on the compressor unless You have access to a field start kit for motors/compressors, if not replacing the relay would be an inexpensive way to be sure its not this common part failure.
As far as replacing the compressor for this unit would cost more than an inexpensive refrigerator could be purchased, and also requires a license in most states to buy the refrigerant. This one appears to be fairly old and would probably require an R12 refrigerant which EPA has highly regulated since 1993 and is very expensive if You can even find it.
So try the relay if it doesnt work then You are still ahead of the game a service call is double what this part will cost You and You will know You need a new frige.
Sorry I forgot the link to the relay....here it is>