Could be the fuel pump? That's what happened to my '90 Burb.
I think the pump is still good. I think it's an electronic issue. Sometimes with key "on", everything works and the pump will prime, then when I try to start it, it won't crank. I try it again, and then the door buzzer and pump won't even work. I replaced the ignition switch and ignition control module, but still no luck. Regardless, the lights all work, but the power windows won't. Maybe it's a ground issue, maybe it's an ECU issue? I'm going to dig around on here and see what I can find, and maybe start a thread about it if I can't find anything.