It is possible for your refrigerator to work when your freezer does not. Refrigerator-freezer appliances have independent controls which can malfunction separately. If your refrigerator is fine but your freezer seems broken, there are several things that could be wrong.
This is one of the most common problems with freezers. The temperature may be set too high. Lower the temperature on the freezer's thermostat, usually located inside the door or at the back of the freezer. If this does not correct the problem, replace the thermostat.
The freezer fan, which circulates air over the cooling coils, may not be working. Locate the fan in the back of the freezer section, and check to see if something is keeping it from turning.
The condenser coils, located underneath or on the back of the appliance, get rid of heat. If they get dirty, the freezer may not be able to cool properly. Unplug the unit, and clean and inspect the coils.
The defrost timer may be stuck. This is usually located behind the front grill of the freezer or behind a cover plate inside the freezer. To test whether it is simply not advancing during cycles, unplug the appliance and turn the timer screw clockwise until you hear it click. Wait half an hour for the freezer to cycle to cooling mode. You should hear the compressor motor running. If it is not, replace the timer.
The freezer door seal may not be sealing correctly. To check, insert a dollar bill and close the door. When you try to pull the bill out, you should feel resistance. If it slides out easily, your freezer is probably not closed tightly and the seals need to be replaced.