Look at the threads that show how to check and replace the "blend door actuators" - one or more is probably bad. The compressor won't engage if the refrigerant pressure is too low. Also be sure to check the setting and operation of the HVAC head (the AC controls in the car). Be sure you know what the temperature is set to. You can set it to 60F to force the blend doors to move to AC only. IF that works there is a chance that it's just the temperature sensor in the dash that's gone bad (Rarely). Easiest way to check that is with a thermometer in the passenger compartment that you can compare to the sensor's temp reading, which you can get to using a GM/Vetronix Tech II scanner or Car Code (a code reader won't).