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Use the key to start the car and turn the air conditioner on high.  Feel the air coming out of the air conditioner and assess how warm, cool, or cold it is.  If the air is warm to cool, but not cold as it should be, there may be an issue with air flow.  Check to see if the cooling fans on your radiator are running.  If they are not, there may be an electrical issue. You may need to replace the cabin air filter in your vehicle to increase air flow. You will need to ensure the air conditioner compressor is working to determine the correct course of action to make repairs if necessary.  Locate the air conditioner in the engine bay and look to see if the center of the pulley is turning along with the pulley itself.  There is a clutch that engages when the air conditioner is working.  With the clutch engaged, the middle of the pulley will rotate along with the pulley itself. If the clutch does not engage, the A/C compressor may be broken and require replacement or it may just need to be filled with refrigerant. Most compressors have a wire leading to the electric clutch. Find the connector in the middle of that wire, and unplug it. Take a length of wire and run it from the compressor's wire to the positive (+) terminal of your battery. If you hear a loud CLACK, the electric clutch is functioning properly.  If not, it will need to be replaced.  Replacing your A/C compressor may require specialized tools. Bring your vehicle in for repairs if the compressor or clutch needs to be replaced. You can purchase leak detection kits to help you identify any leaks in your air conditioning system.  These kits provide a dye that will run through the lines and seep out of any leaks or cracks, making them visible to the naked eye.  Connect the leak detection can to the low side service port and spray it into the air conditioning system. If you spot any leaks, you will need to take the vehicle in for repairs. If you do not spot any leaks, the problem may simply be low refrigerant.
Start the vehicle and turn on the air conditioner. Look to see if the A/C compressor is running. Check the wiring leading to the A/C compressor. Look for leaks in the air conditioning system.