In short the problem with my dead Bimmer (1987 325e no spark) was the DME Motronic control unit. That was for those that don't want to read the following.
First of all I would like to thank Chris (parts); Dewey, Jeff, Erik, Jimmy, and Harvey (advice on fixes); Mastura (support).
My car wasn't giving a spark, so I grabbed the Bentley and started at pg. 1 of the Ignition system section. I know the plugs, wires, distributor cap/rotor were all replaced within the last 8-10 months and I was assuming they were in good shape still. I checked battery power reaching the coil, which was there, but no spark from a spark plug wire to ground or the coil to distributor wire to ground either occured. Checked the resistances (primary/secondary) of the coil and they were fine.
Posted a message to the digest while continuing my tests. I tested the main relay by looking for battery voltage with my high input impedance DMM at a fuel injector connector with the ignition on and saw the voltage there. Also felt for the clicking of the main relay when ignition turned on. Both tests o.k.. Decided to check the fuel pump relay, because the fuel pump wasn't coming on when the ignition was turned on like I think it should for 2-3 seconds. There was battery voltage at the fuel pump relay, but no signal from the main relay. I just checked the main relay, though, and it appeared to be o.k.. At this point I started thinking about the DME as a cause, but I got two tips that the problem could be related to the reference sensor or speed sensor on the car (325e..."i" cars have a pulse sensor instead). I found the connectors and checked the resistance of these and it was within 2% of the spec value.
I decided to check for signal at the DME figuring that if the main relay signal was reaching the DME Motronic unit, then maybe the DME was bad. I checked for signal and sure enough the main relay signal was there and everything else looked o.k..
At this point I had no conclusions, so I started looking for used parts to swap in, since I couldn't afford the new parts all at once. THANK YOU CHRIS KENT. He gave me a package deal of some suspect parts out of a wrecked 325e and got them here with next day delivery! Today, I swapped in the DME and the car started right up! I plan on opening up the old DME and looking around for bad solder connections. Once again this digest and my Bentley have saved this poor graduate student some big bucks in labor and parts.
Thanks again everyone for your help,
Case Western Reserve Univ.
1987 325e 117k miles