There's a number of things that could cause this, but since the computer isn't throwing a code, it most likely is the fuel pump.
If it IS the fuel pump, I remember reading something about pulling up the carpet in the rear and CAREFULLY cutting an access port through the floor that greatly simplifies the fuel pump replacement process, now and in the future. You'd then fabricate a cover that you attach with a few sheet metal screws and some sort of gasket under it.
This procedure was for the 1st-gens, but I'm pretty sure it's applicable to the 2nd-gens as well. Someone can probably provide measurements so you know exactly where to cut, and how big. Be careful cutting the hole, since the gas tank IS right under it.
"Ahab knew, baby...I lust." -- Vet-san
1990 Dodge Caravan SE, 3.0L 3-speed, 130,000 miles
1995 Plymouth Neon, 2.0L SOHC base model, 134,000 miles
2004 Honda Element EX, 70,000 miles