I wrote in another forum:
Here's a short list of how you can check your air conditioning system yourself...
First, you'll need a multimeter.
The most important thing is that the air conditioning system is properly filled.
If it is, the low-pressure and high-pressure sensors must be delivering the correct readings. You can measure this with a multimeter. The low-pressure sensor is located at the back of the engine bay at the dryer cartridge in the low-pressure line and must have continuity when the system is sufficiently filled.
This is the most important thing, because air conditioning systems usually contain too little refrigerant, and then this switch shuts it off.
The high-pressure switch is a bit more difficult to measure, but it's not rocket science either. It shuts off when there is too much refrigerant in the system, which is rarely the case.
The high-pressure sensor is a pressure sensor and delivers different voltages to the control unit. With the engine off and the system properly filled, it should deliver between 1.2 and 1.7 volts. You need to measure the black or blue wire against ground.
If these two conditions are met, then your air conditioning system should be able to be engaged via the climate control unit.
If that's the case, then power is reaching the base of your magnetic clutch relay. You can easily measure this with a multimeter. If that's the case, then power must be reaching the connector at the bottom of the air conditioning compressor. If that's the case, then the magnetic clutch must be engaging.
You can check the magnetic clutch by measuring the resistance. Resistance must be 4 Ohm.
That's how I would proceed logically in your situation. If the system is properly filled and the pressure switches aren't defective, then the system should be enabled, and if your climate control unit isn't defective, then there should be power reaching the magnetic clutch relay.
The diagnosis is not so difficult...