Fuel system- 2000 olds Alero

My wifes car began not starting about a weak ago,
thought it was just gas freezing, not starting again so we reset by pulling the hot wire on the battery it worked, but the next time she went to start the alero the engine tuned but no start (I
did not hear the fuel pump pumping. So we replaced the feul pump relay and reset the cumputer, it worked ! We thought. We did here the pump and the car started. But the next morning no sound of pump and no start. When we tried the reset thing again we get no fuel pump
noise any more. So my Question is were should I
go next. Filter, sensors, pump ect. Ect.

OH! When we pulled out the old fuel pump relay switch it was caroded on the contacts, so we cleaned board best as posible
Thanks
Richard