An easy way to test the fuel pump and filter is to disconnect the fuel feed hose from the fuel rail and connect it to a long length of spare hose with the other end draped over the fender going into a catch can placed on the ground. Now turn the ignition key to the run position but DO NOT TRY TO START THE ENGINE. You should see fuel going into the can at a good rate for several seconds; you can also do your "jump a wire trick" by running a wire from the positive (+) battery post to the (+) side of the fuel pump harness connector, then you should see fuel going into the catch can at a good rate.
Check the fuel pump fuse #50 in the IPDM first. Use a test lamp or voltmeter to make sure it has power, don't just check visually. The fuse is north of the relay, so it should have power anytime the key is on. You can check the pump directly by jumping 12V to pin 39, it will be a Black/Yellow wire. Pin 39 should go hot for about 2 seconds when you turn the key without starting the engine, or stay hot during cranking or when the engine runs. If the terminal doesn't go hot, try swapping the fuel pump relay with the fog or headlamp relay. If that fixes it then the relay is bad, if not the IPDM may be bad or there's a problem with the ECM or wiring. In that case, post back and I'll tell you what to check next.