1993 Ford Probe Probe won't start, possible fuel pump?

Engine Mechanical problem
1993 Ford Probe 4 cyl 150k miles

My water pump went out on me and I just finished replacing it and putting everything back together. Now, my car will not start. It will turn over but it just won't quite get there. As it is turning over you can see the "fuel cutout" light blink as you can hear fuel burn just a little. I have been able to pump the gas and kind of have it run very very badly. Once I stop doing that, the car shuts off. The spark plugs, distributor, starter, and battery are all good. In the past I have had problems while driving the car. Sometimes it would not start, then it would magically start one day. Other times while driving, If I throw it in neutral or have the clutch in it will die (fuel cutout light comes on). While driving, I can drop the clutch while in gear and it comes right back on. As long as I have it in gear it would not die. Very annoying for stoplights and stop signs as I would have to keep gas going to it. I can hear the fuel pump come on when I turn the key but barely. I'm pretty sure it was a bit louder than I am hearing it now, but I can definitely hear it coming on. Is it possible that my fuel pump is dying? Would a fuel filter be a problem also? I have to drop the gas tank in order to change the pump. Is there any way to troubleshoot this to figure out exactly what it is?