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Pull the center console and the shifter boot and see why it wont shift. There's a cable for the ignition switch to unlock the shifter. Is it functioning when you turn the switch to RUN???
Does the shifter handle move at all or is it locked in PARK??
C5 with A4s have issues with the selector switch on the drivers side of the trans. The plastic fitting that connects to the shaft and cable can and do break.
Access the shift lever under the shift boot and disconnect the single connector going to the solenoid. If the cable to the ignition switch is not at fault the solenoid is most likely the culprit.
See my posts several years back for details.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.