Remove the taillight assembly (click here for instructions ), there are two hex head screws that hold the lock bracket. You must then get under the car to unplug the electrical connection.... this is impossible to do without removing part of the screws that hold the black plastic panel under the back bumper.....enough to get your hands up in there to unplug the connector.

If the key goes in the lock and it turns, then the problem is probably the electrical switch on the back of the lock. I believe you must purchase them as an assembly from GM but if you can find one in a wrecking yard or contact Jim Finn

You can keep your lock and key and just replace the switch.