'90 Vette conv. doesn't stay on?

This is 1990 Corvette convertible with a manual 6speed transmission. It starts but won't stay on. Now the last owner changed/ replaced a lot of things dealing with the fuel. He thinks 2 of the fuel injectors might be the problem. I am the new owner, first Corvette, and don't know nothing about fuel injection, but first thing I'm thinking is if might be efi(electronic fuel injection), computer/ fuse and or ignition switch. Yeah that reminds me owner did mention something about getting it a new switch. I checked it and it looks like halfway out the steering column...