It may have a start or a run capacitor or a combined start/run one
a small black can near the compressor with wires going to the compressor
they are a common fail point and cheap and eazy to replace

Any part you have to buy is going to cost upwards of $50, so keep that in mind before you put a lot of time into diagnosis. One cost-free possibility is that the condenser coils are clogged with dust/lint/dog hair/cat hair etc. They are under the fridge on the left hand side. Clean them with the crevice tool on the vacuum cleaner.
That's it for the freebees.
If you contemplate putting money into it:
There is a condenser fan behind the cardboard panel on the back near the floor that should be running when the compressor is running. It cools the compressor and the condenser and if it's not working it can cause the symptoms you describe.
If it's OK, check for a frost-clogged evaporator. The evaporator is under the floor of the freezer. Take out the plastic guard over the evaporator fan in the center of the floor at the rear. There are 4 phillips head screws on the sides and near the back that hold the floor in place. Take it out and make sure the coils are free of frost. If they are, plug the fridge in and run the compressor. There is an evaporator fan at the back of the freezer that should be on when the compresser is running, if it's not it can be your problem. If it's running, throw a towel or something over the coils to insulate them a bit. If the coils get evenly cold after about 20 minutes the sealed (freon) system is working so you don't have to worry about that. If only one end of the coils get cold, freon has leaked out and it's time for a new fridge.
If the evaporator is frosted up, defrost it and check the defrost heater - it's a long glass tube with a heating coil in it located between and below the evaporator coils. If it's broken, it's bad. :rolleyes: If it isn't, take a flat blade screwdriver and rotate the rotor in the defrost timer until you hear it click. The defrost timer is a black box about 3"x3" in the front near the floor. There is a round "thing" on the front that you can turn with flat blade screwdriver. Turn it clockwise until it clicks, which should turn the compressor off and the defrost heater on. If this happens, the timer is not rotating itself and needs to be replaced.

This is my bet as well. But the R-12 to recharge it will cost more than a new refridgerator :eek:

Might be time. Your new one won't last 40 years however.

Check with the local utility, sometimes they give a $50 rebate for old ones, and haul it away for free.