My 1990 Corvette first started hesitating on full throttle. I replaced the fuel pump and filter. It was ok for a few days. I drove it about 50 miles. Stopped for 10 min. then restarted. As soon as I cleared the on-ramp to the freeway the engine quit. I had to have it towed home. At home it would not start. The next day it would crank, start, run for 1 second then die. I would not start again that day. The next day it would start, run for 1 second than die. It would not start again.
I removed the fuel pump and tested it--it runs. I re-installed it. Same result: start, run for 1 second then die and not re-start.
There are no trouble codes stored--just 12.
What could be wrong? What should I test? I am a good mechanic, but I don't understand the car's computer controls.

You should check the fuel pressure first. You may have a bad fuel pump relay(s). Your fuel pressure with key on engine off should be around 43psi. With engine running, it will drop to around 38psi at idle.
Also, disconnect the air flow meter(if your 90 has one) to see if it will start and run. If it does, the air flow meter could be dirty, or bad. Do the same with the TPS.
Pull a plug wire and see if it is firing while you crank, too.