Its very common for these cars to spring an AC leak at the evaporator. Hows the airflow to the vents?
Turn the front of the compressor, right in front of the pulley. If it turns, its probably not turning on due to low pressure. One way to check for sure, is to unplug the low/high pressure switch at the accumalator, and short the wires together (Paperclip?). Turn the AC on, and the compressor should spin up. If it doesn't, you'll need a schematic of the wiring to test for power to the compressor. If it does , the system is low on the refrigerant.
2009 Pontiac Vibe AWD 2.4
1993 Buick Park Avenue 3800
1984 Chevrolet Citation 2.5 liter four.