You 2 are playing with fire "jumping" fuel pumps etc. What a waste of time and you are not finding anything out as far as diagnostics go. These cars need a steady 12+volts to operate. Start with a good source(battery/alternator) than go from there. Your statement of removing the blower motor resistor and it not helping. Did you do a amperage draw before and after? Not trying to be a jerk here, but you are asking for help, we are directing you on what to do and you continue to take random stabs at solutions. We are all in support of DIY, but this can also be a great source of learning if you will follow the lead of others who have been there. These are expensive cars and they need to be dealt with accordingly using the right methods/tools/diagnostics. Jumping fuel pumps from a battery post is NOT the way to go about it.

__________________
Dave S.
Northeast
2003 4.6is
2005 E53 4.4
2003 E39 Msport(a REAL ONE!)
1959 Fiat 600