If the key goes in the lock and it turns but the trunk does not open, 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. You may be able to find one in a wrecking yard.

Remove the taillight assembly: Click here for instructions.

There are two hex head screws that hold the lock bracket in place. You must get under the car to unplug the electrical connection. In order to unplug the electrical connection you must remove some of the screws that hold the black plastic panel under the back bumper. Just  remove enough screws to get your hands up in there to unplug the connector.
{xtypo_info}You can keep your lock and key and just replace the switch.

Thanks to Barney Eaton, member of the Reatta forums, for this information.