You have a new battery and your key fob batteries are new. I'm speculating here that your VATS (Vehicle Anti Theft System) has been activated and is putting up a lot of absurd responses to the violation of the security system. The examples are clear- alarm doesn't sound, door refuse to open- these are BCM (Body Chassis Module) issues yet the Corvette starts up and runs. These events sound bizarre because they are supposed to in order to get your attention. GM is very secretive about the VATS function. If someone or something has made repeated attempts to steal your Corvette, each attempt causes the VATS to dig in deeper and shut down more and more functions. I'm not completely sure of this, but when a battery is changed, voltage drops to zero, and VATS is activated. I believe the GM technician will use their Tech II diagnostic tool along with tech support via the internet to enter a code telling VATS that a battery change was performed and that all is well with the Corvette. GM knows that eventually you will take the Corvette to the dealer because outside of GM, very little is known about the VATS system- if VATS function was made available to all repair shops and mechanics, then eventually the bad guys would know how it can be defeated. It is so effective, that every push button start GM vehicle cannot be stolen because of the programmed VATS shutdown of the various computers in the car. So, call ahead and make an appointment to have the VATS system reset.
