Sounds like you have a short in the coil pack harness somewhere. I'd bet it's in the wiring harness near the coil packs. They tend to flex when plugs are changed. Pull the DME connector and test all coil wires. I'd do a continuity test, then a ground test, then look for 12v on all wires with the ignition on. You might have to manipulate the coil harness to cause the short.
Each coil plug has three terminals. According to the E30 ETM:
Pin 1 on each coil plug is the "floating" ground for each coil primary. Should be a black wire, although hard to tell since it's shielded co-ax cable. It's a grounding wire, but it doesn't ground to the chassis at all. It runs directly back to the DME instead. Coil #1 goes to DME pin 25, #2 to pin 52, #3 to pin 24, #4 to pin 51. If I recall correctly, the DME switches the coils on those floating ground wires...it has four big MOSFET driver transistors to handle high current for that purpose. The shielding jackets are grounded to chassis at the passenger shock tower.
Pin 2 on each coil plug is chassis ground, runs back to G103 on the passenger shock tower. It's shared with DME pin 26. Might be a brown/orange wire if an E30 donated the wiring harness.
Pin 3 on each coil plug is the positive wire for the coil primary. Should be green, and should see 12v in either start or run positions.