AC Problems.......
There is another quirk with electronic a/c and that involves a relearn function when memory power is removed from the system (such as disconnecting the battery). Once repowered, the blower doesn't function and the temp door is cycled from fully open to fully closed. This allows the Programmer to learn it's position, electronically, and after about 2 or 3 minutes, everything should function normally. But, if you are seeing zilch at start up, then suspect that the memory power supply has an intermittent open. I don't think this is what you are experiencing, but I thought I'd mention it just in case.
I don't have access to complete Service Bulletins for your '96 but the only one I found was a revised diagnostic chart for the blower motor. Would hope that your Dealer checked for any and found none, but you might ask him or some are listed at www.nhtsa.gov
The only other thing you might want to check is the vacuum tank. Apply 10" of vacuum and make sure it holds.
I had a similar problem on my 94. All the air would come out the defrost for a minute when I started the car then it would slowly switch to where it was set. Turned out to be a vacuum leak in a check salve near the fuel rail.
The Best of Corvette for Corvette Enthusiasts















