One way you can check the fuel pump is to listen when you turn the key to "run" (before "start"). You should hear the fuel pump kick in briefly and pressurize the line. My wife has a cousin who used to have a mustang, early 90s I think. But anyway she'd get this problem all the time, and what she'd have to do was go open up the hatch and reset the breaker. This happened one time while I was there and I said, "What the ? You have to flick a circuit breaker in your trunk before you can start your car?" I didn't believe it until I actually saw it.
But anyway, you turn the key to "run" and you should hear an electric motor whirring noise from the gas tank for about 1 second and then it'll stop. That's the sound of the fuel system becoming pressurized and ready to start.
My 2 cents...