So that wire runs from the battery to the computer?
which wire? Pin 1 on the computer's wiring harness is constant battery power.
the FP relay wire you are having issues with sounds like the ground from the computer to the FP relay.
I was thinking that someone might chime in about how to remedy the FP relay, but no one really has. If you search TMoss' old posts (or search for people with computer and/or no fuel pump activation issues), there was a thread some time ago where Tom was talking about remedies for a lost FP ground pulse. (I might have just grounded the wire, but did NOT want to suggest that since I dont have a mastery of the system like others do).
BUT, now that you also have this issue, I would get access to the puter (remove pass kick panel) and start probing terminals to see what is going on (now that you possibly have a couple inputs and outputs not doin what they should be). Your puter might have taken a poop, but you need to be real sure that the wiring is sound before you put a new one in, or you can fry the new puter. Jrichker, TMoss, et al are much better at this stuff than I.
My two cents.