Problem is either a pinched fuel line, clogged fuel filter, or your USED fuel pump is total junk. Could also be fuel relay. Should be under the hood. If I were you, I'd check the relay first. When you turn the key to the "on" position, the relay should click. If it does, then it's still good. Check your fuel lines. Make sure there's no pinches in them. Replace your fuel filter. It doesn't cost much. 20 bucks average. Then atleast you know it's new, and will not be your problem anymore. Another thing, why did you buy a used fuel pump? I can understand not having much cash, but getting one brand new you know what you have. There's no question that it'll work. Buying used parts that are essential for the car to run is inexplicable IMO. But start with what I said. Start at the front, and work your way back.
1999 Chevrolet Camaro SS (PC'd)
1994 Chevrolet Beretta Z26 Q4 (W41 M90'd)
2004 Chevrolet Silverado 2500 (4WD)
My wife's cars:
1971 Dodge Charger SE (stock and original 383 auto)
2004 Subaru Impreza WRX (kid-hauler)