Just posting in case someone comes to this thread in the future.
From what the OP has stated, the heater is not working. If the heater is not working, it would have nothing to do with the compressor.
Lest there is some random compressor I don't know about installed on your cooling system, then the only compressor I know of is for the A/C system. This compressor works by compressing refrigerant, which makes it hot, then letting it expand which makes it cold. That cold air then has a fan blow over it and you get cold air in the cabin. So that's the A/C system in a nutshell.
The cooling system - the part that cools the engine - has the radiator, some hoses. water pump, coolant (or antifreeze),thermostat, and a heater core. Depending on the engine installed in the Impala, the heater core may not be getting enough coolant. Just as the A/C system moves its 'cold air' to a spot where the fan van blow it into the cabin, the heater core moves hot coolant into a place where the fan can blow it into the cabin.
To ensure that the heat for the cabin works properly, you need to make sure that the engine is up to temperature, there is coolant (obviously), and there is no air trapped in the system.