2000 Mercury Cougar Fuel issue?

The car has had problems in the past with dying, and not restarting unless you jiggle the connecting wires. (This is coming from a friend, haven't experienced it myself. There might not be a wiring problem, maybe by just letting it sit.) The car used to die all of the time, low gears, high gears, idle or in motion. We have replaced it with a compatible fuel pump, not one designed for the car, but it seems to work. The car won't die when idling now or in low gears but it sputters heavily in fourth and fifth gear (the car is a manual). The car generally just seems to be low on power most of the time too. Any advice? I am curious to know if it is a spark plug or the fuel injector, and replacing the pump only seemed to solve half of the problem. Any advice would be appreciated. Thanks!