Hello,
it sounds like you are having a defrost issue. Look in the back of the freezer compartment on the rear wall to see if there is any ice or frost build up. If you can't see any press on the rear panel to see if it gives a little. (2nd)If it doesn't give or if there's ice/frost, unplug the unit, take everything out of the freezer and remove the rear panel, if you see a lot of ice if so you have a defrost issue for certain. If so you can use a hair drier to thaw it out or a steamer fi you have one. Look above and below the coils you should see a glass tub with a coil that runs thru it (that's the defrost heater) if it looks like a burned out floresant light thats probably your problem. If not look for the defrost thermostat( it's a small round thing about the size of a quarter and about an inch thick, use an ohm meter to check for continuity, if there is continuity there.

Try this first. It's probably the defrost control which is behind the consumer contols in the refrigerator side. It looks like timer and should have a little dial on the front. Slowly turn the dial until the unit shuts down. In about 10 min. you should hear ice popping and maybe a sizzle noise, and it should kick back on in about 30 min. If this works then your good for a few days. And you know it's the defrost control. If not then it is probably either the heater or the thermostat.
Hope that helps
Nat

If there is frost build up inside the freezer then it has nothing to do with the compressor. Most likely the problem is a faulty defrost system as Nat told you in her reply. Follow her troubleshooting instructions and post the results.

Here are the break down diagrams for the Hotpoint refrigerator Model CSX22GRBKWW

Gene.