I have an electrical problem with my jeep cherokee 1996 4.0 6cyl, what could it be?

Ok so here I have a 1996 jeep Cherokee
classic 4.0 6cyl. Im going to describe in
order of events.Here are the details. Jeep
was running fine till one day It just wouldn't start.. I'd cranck it and nothing. My first
thought was the fuel pump...I tried to hear it
and nothing. Of course I checked the relays
and and i checked the fuel pressure up top
on the fuel line and rarely anything was
coming out but just drops as someone else
primed it and crancked it.. (I did have gas).
Went to go buy a new fuel pump and filter.
I put it on and the jeep would start but I'd
have to press on the gas a bit for it to stay
on. Driving after a while it ran all day the
way it used to. Then things got weird. Days
later i woke up twice with the battery low
almost dead. I know i wasnt leaving anything
on. Took the battery in to get check and
well it was going bad and I'd have to get a
new one. Bought a new one but before i got
the new one, i was running on a back up
battery that i had and with that one the
jeep would start quick and i didnt need to
press on the gas pedal for it to stay on
unlike the other battery. Before i got my
new battery one morning the jeep wouldn't
start. I replaced the battery
with the new and still wouldn't turn on. Took the fuel
pump in just to be sure i didnt get a bad
one. I had warranty. The new fuel pump
wouldnt come in till the next day so i was
stuck home. I did the volt test to see if was
getting a drain somewhere maybe and well
nothing. I had some one move the ignition
as i checked with a multimeter to see i was
getting power to the back where the pump
is and i had none going through. I grabbed
my old pump and hooked it up to my
battery and it turned on. I hooked it up to
the line where the pump connects to in the
back and had someone move the ignition for
me and nothing. Again I've replaced the
relay. So i give up for the night. Next
morning i try the same thing and while i
hook up my old fuel pump and try it again
this time it did turn on. I put everything
back together. And the jeep turns on. There
i go to go get my new fuel pump and well i
haven't replaced it. I still have it and the
jeep is currently running on the old one. I
dont know what to check or do next time it
happens. Here's the other thing...there are all
kinds of connections and other gas looking
lines that lead to no where. I find out from
the previous owner that the jeep used to
run on natural gas and got converted back
to gas. It has this weird processor box under
the hood I wondered what the hell it was
for. He said he had the same problem but
that it was "intermittent" and that he
replaced everything I had done except for
the battery and he couldn't pin point what it
was. He said the problem just went away.
The check engine light works but it's not
showing. He said that the whole computer
box for natural gas or whatever its called
was cancelled. I checked all these dead end
connections and there is power running
through them. Right now its running fine but
I'll probably take it to a mechanic. What do
y'all think?