When the compressor doesn’t turn on at all, it can mean a couple different things. You are either too low on freon, you have a power/ground issue meaning the compressor isn’t receiving the signal to turn on, or the clutch itself is bad. You will need a set of AC pressure gauges to check the following. Click on the image to get more detail on the gauges. This set costs about $35.
First thing is to start with checking the freon pressure. Static pressure will give you a good idea if the system has enough freon to tell the compressor to turn on. Hook up your gauges and record the static pressure. Depending on the ambient temperature (air temperature of outside atmosphere), the static pressure of a full system should be around 90-110psi assuming you are checking the A/C when it is actually hot outside. If the static pressure is 50 or lower, the system is definitely low. You will need to evacuate the system and recharge it to the proper levels and retest. If it 150 or higher, it could be over charged or there is air in the system. Same result, evacuate and recharge the system to the proper levels and retest.
If the static pressure readings are within spec, you can evacuate and recharge the system anyway (it never hurts to service your AC system) just to positively eliminate a freon level issue. But likely, you will need to dive into electrical diagnosis from here. Follow the link below to get a good electrical flow chart.