1994 ZR1 Starting Issues

I have a 1994 ZR1 Corvette with a 6 speed which starts fine when cold, but once you drive it for a while and shut it off it goes totally dead--not even a click. You can push start it so that pretty much eliminates the security system. If you let it sit for a hour or so and it cools off--it will start right up. Some people have told me it could be either the neutral safety switch or the starter. Has anyone had this same issue on this exact car? If so how did you resolve? :uhoh: