If you jumped the power contact at FP relay ...
and car starts and run fine, + to FP relay 86 is OK and, and relay itself is OK, my only guess is that DME output transistor is damaged (or the contact at pin one of DME got bent or some how damaged in the connecting / un-connecting work you have been doing lately). The only sensor I know of being capable of shutting down the pump is the CPS, and it acts as a permissive for the pump, the engine is required to run in order to keep pump working, after the initial prime due to the key turn, when it would run briefly with the engine stopped. If it does not do that, sorry, DME output at pin 1 should be checked.
Javier
Electrical Problems: 0 . . . Amatuer Mechanic (with bimmer.info help): 1
250V 5 amp fuses for my dad's multimeter: $6
DME/Main relay with shipping: $17
Crankshaft position sensor two day shipping from AZ: $105
Successfully starting my car after 4 weeks of troubleshooting and repair but having to get out of the car immediately afterward so when I wet my pants I wouldn't ruin my leather seats: Priceless.
I pulled the DME and looked in vain for burn marks or signs of damage. I replaced it and turned the key but the pumps still didn't run. Resigned that I would not be able to get a DME any time soon, I tested if my jerry rigging job would trip the relay and it would. I then ran a wire from fuel pump relay socket 85 to a ground. When I cranked the engine I flooded it. So I promptly removed my hack job and cranked until the engine worked out the extra gas. I assumed the engine would eventually die but it never did. So I tested for voltage at the fuel pump fuse: 12v, no complaints. I let it run for a little while, double-checked that my hack job was removed, and shut of the engine again. Then she started right back up and ran like a dream. I heard a disturbing noise for the first mile but then I pulled the hand brake and cleaned the drums. What a relief.
I assume when I pulled the DME it reset??? I'll let you know if it brakes down tomorrow.
You guys have been great. I bet you were hoping this thread would end about 30 posts ago but I think the ending makes it all worth it.
Please allow me to at least thank everyone who chimed in: ryan roopnarine, 632regal, DanDombrowski, Garlic Breath, genphreak, SSR2, Bellicose Right Winger and especially lowell, Bill R., Javier, and stevebuk
I know you guys are going to help me enjoy this car for a long time; you already have.
It is great to know!! Thanks for your feedback.