In that case wire is wire. If it wouldn't run with the spliced-in piece, it either wasn't really spliced (no connection in the splice) or something else has gone intermittent. That's what seems to be the case with your situation. Most likely the fuel pump relay. I don't see anywhere that you've said you replaced it with a known good one.
Quotes to live by:
guessing gets expensive
nothing is more expensive than a cheap BMW
buying a ratty example (of a BMW) is a parasitic relationship.(and you ain't the mosquito)
Ken Kanne, Silverhill, AL, E36 Forum Mod/Craigslist addict/Hoarder of all sorts of stuff
1995 318is "Bebe"; 1993 325is "Elvira"; 1985 635CSi "Katja"; 1984 633CSi "Sylvia"; 1987 325is "Odette"