There is only one compressor. The good news is that the a/c system should be working fine if you get cold air in the front system.
For 2002, there are manual and automatic controls for the rear system. The manual system is simply a potentiometer that provides a voltage between battery and ground to the temperature door motor. Look for a wire that has rubbed against aand shorted to ground.
The automatic system uses an infrared sensor to determine the temperature in the rear seating areas. This could be messed up. There should be a manual mode to allow you to determine if the control head works at all, the IR sensor is bad, or if the head is fine. Set the system to manual and try moving the temp knob. If it doesn't move, look for a shorted wire to the temp motor. Or measure the voltage at the motor to see if it changes.
Other possibilities include a stuck temp door.
A Personal Experience:
Our 2003 did the same thing. Was the first Tahoe I'd owned and did'NT know alot about the a/c system. In fact , I figured since it didnt blow cold BRAND NEW, then it wasnt supposed to. Years down the road a friend asked why it didnt blow cold, so I took it to a REPUTABLE mechanic. Turned out to be a bad Rear Condensor.
My 91 Shadow with 100,000 miles had the same problem. Ended up changing the front struts, motor and transmission mounts. Problem solved.AnswerIf the clunk is not very loud, the problem could be that the front stabilizer bar bushings are worn or hardened. i have an 89 that did the same thing . it was the struts.
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