There is a lot of great info in this thread!
I just wanted to clearify (maybe) the function of the DME relay.
DME Relay is actually 2 relays inside a single housing. 1 section powers the DME system and 1 section powers the fuel pump.
Here are the wire descriptions and there functions, as best I know.
Note: You may have to unplug the DME relay to read the terminal designation to determine the wire positions.
T30 - 4mm Red wire from the battery, provides power to the relay for DME system. Everything powered from the DME relay goes thru these wire.
T85 - 1mm Brown wire to ground
T85b - 1mm Black/White wire to pin 20 on DME Control unit (DME grounds this to power fuel pup)
T86 - 1mm Black wire from 15 circuit, 12volts with Key ON AND while cranking. (From the ignition switch)
T87 - 6mm Red wire to DME Control unit, injectors, idle control valve (power out of the relay)
T87b - 2.5mm Red/Green wire to fuel pump (power out of the relay)
also .75mm Yellow wire to O2 sensor heater (later cars)
Power from the ignition switch in the ON position AND in the start position goes to T86 on the DME relay. If T85 is properly grounded the relay then outputs power to T87 to the DME and injectors etc. It also provides power internally to fuel pump portion of the DME relay and when the DME control unit grounds the wire to T85b the DME relay outputs power to T87b to the fuel pump.
To me your symptoms seem like the wire to T86 at the DME relay is not getting power while cranking, only while in the Key ON position..
But never under estimate the havoc bad grounds can cause and double check them all.
Jim