Car will not come out of park
Apparently a common problem with the C6. It appears to be caused by a bad shift interlock solenoid. You can find DIY instructions on about any Corvette forum. Here’s an example: https://www.corvetteforum.com/how-tos/a/c6-corvette-why-is-my-corvette-stuck-in-park-368439
Is your brake lamp switch working?
The vehicle may need to recognize you’re stepping on the brake pedal before allowing you to move out of the park position
A friend of mine has a 2008 Corvette and it once had the same problem. Along the lines of what db4690 said, it turned out to be a bad brake light switch. While it is a doable DIY job to replace the switch, we had to take it to the dealer to have it calibrated. I’m not saying that this is what is wrong with your Corvette but it is a possibility.
My car has been doing this for years. Problem only occurs when parked nose up. I happen to have an uphill driveway. As someone mentioned earlier, there is apparently an issue with the car not recognizing the brake being on. The guy next-door, who’s jeep did this taught me a quick fix. It’s a bit of a pain, but whenever it happens, I just go behind the car and rock the wheels a couple of times. Then I get in and the car shifts perfectly.