88' XJ starts, runs, sputters to a stall?
 

...To start out, my jeep is an 88' Cherokee with a 4.0 auto, stock besides a ZJ tank and fuel pump raised into the cargo area...

Ok, well my jeep decided that it doesn't want to be streetable yet. Today it started just fine, ran for a second or 2 and died. That's all it would do. If I start it and rev it up, it would rev up for maybe 2-3 seconds and die.

Well we went ahead and replaced all of the relays on the passenger side inner fender, and all this accomplished was making it start, run for 5-10 seconds, and then sputter and die. We tested all the wiring and after a bit we figured out that it gets full power when cranking, and it primes when you first turn the key on, but after it starts running and you return the key to the run position the power kind of just fades away. We jumpered a power wire straight from the battery to the pump and it ran awesome. Where do I Need to look now? Any ideas?

check this resistor its bypassed when starting but pull the contacts and connect them then try to run it
its on your drivers side fender wall near the air box
Attachment 44677

Should I just try bypassing that? Basically just connect the wires going into each side?

Yea that would work

Ok, well I bypassed the ballast and it runs great. I bought a new ballast from napa and when installed it still does the run and die thing...so I stuck a 10 amp fuse in the wire terminals and wrapped it in electrical tape for now. So, how important is the ballast resistor? Am I endangering anything by having this bypassed?

I believe all it does is quite down the fuel pump so no it shouldn't kill ya

id agree that your fine runnin w/o the resistor. generally, like the name implies, the resistor limits the power/current/flow, etc. going through it. so by bypassing it, you are running a signal at full srtength. the closest i can think of is the blower motor resistor for your fan. on 1-3 its using the resistor to limit air flow, on 4 the resistor is bypassed and it runs full strength. id wanna double check my facts though- if you do damage.. well, its never good... idk, my .02...