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There have been more than a few brand new C8s that had electrical glitches because the battery had discharged a good bit during shipping. First thing I'd suggest is put it on a float charger until it says fully charged, then see if the problem recurs.
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.