The GM key fob has no tactile feedback, it reacts slowly and the rubber caps wear out. Fortunately, someone has reprogrammed VW key fobs to work with GM cars - and the Corvette C5.
You have to cut the stock key in half. Make sure that you don't cut too far down, otherwise the key will not fully enter the ignition lock - making it impossible to turn the key (BTDT).
More information and links to e-bay on the Corvette Forums