Attempt to dumb down what everyone is telling you:
Your engine is Fuel Injected (as opposed to using a carburetor). therefore the fuel system consists of an electric pump, which I believe is located inside the fuel tank, the fuel lines that go from the tank/pump up to the front, the fuel filter, the fuel pressure regulator, the 'fuel rail' that is bascially a tube up at the engine intake, and the fuel injectors that pump the fuel into the motor. The injectors are connected to the fuel rail, the fuel rail is connected to the fuel pressure regulator, the fuel pressure regulator is connected to the fuel lines...
On the fuel rail there is a valve, with a screw on cap (probably blue), looks exactly like a tire valve. One easy way to tell if any fuel is actually even getting up to the injectors, is to take off the cap and 'let some air out' of this valve (just like you would let air out of a tire). Only guess what? It ain't gonna be air. Its gonna be gas, and its gonna want to spray in your eyes, so be real careful.
If there is gas, and if it squirts out real good, you at least know the fuel pump is working, and you have SOME fuel pressure. Is it enough fuel pressure? Ask somebody that bought a gauge.
If you don't have enough fuel pressure, then although the engine may start, and may even drive, it won't always have enough gas and the engine will stall or run bad. That could be caused by a bad fuel pump, or a bad fuel pressure regulator.
The fuel pump just pumps at a constant speed/volume, and its usually way more pressure then the fuel injectors want. So the fuel pressure regulator adjusts the pressure, bypassing the excess, to maintain a constant pressure at the fuel rail.
So if the fuel pressure regulator is bad, it might be bypassing too much, so not enough pressure at the injectors. Or the fuel pump might be bad, never supplying enough pressure for the regulator to do anything with (instead of bypassing, its letting all the pressure staright through, but its still never quite enough). Or it could be a clogged filter, pump can't push past it to get enough pressure at the regulator input.
Since you changed the pump, you know its not that, but you still don't even know if your problem is low fuel pressure or not. Need to verify that first.