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Put new fuel pump in new oil pressure switch and still dies shortly after you start it. The guy I got it from said he was doing about110 in it when it started losing power, pulled over and it died. Then he said it started right up and he went to push gas and it died. Also I noticed that when it starts the second I pushed the gas it dies.
1985 corvettes do not have VATS. I'd run a fuel pressure test - I know you said there's a new fuel pump, but i'd start with the basics.
That's a good idea - hook up a fuel pressure gauge, tape it to the windshield and see what happens when you start it up.
Check the Fuel Pressure regulator (FPR) - pull off the vacuum hose and check for fuel in the line.
You have a 1985 and one area of neglected maintenance on C4s is the fuel filter. I bought a 1996 in 2012 and it had the original filter. How old is your filter? More than ten years and I would change it as a maintenance item.
When the new fuel pump was put in did you change the sock in the tank? A clogged filter/sock at the fuel pump will do that.
You need to hook up a fuel pressure gauge and see what its showing when it quits. If the pressure drops then find out if the pump has power when the pressure drops.
After eliminating fuel as a problem or not post back and we can help with the electrical side of it all.