74 Dart possessed by Satan...

Yep. Your 2nd photo, the ECU. That rusty sheet-metal screw is the only path to ground. Without that, no spark. I don't know why the engineers relied on that (cheap?), but a dedicated ground wire on the case would be smart. A constant issue for many here 40 yrs later.

If that doesn't work, try jumpering 12 V direct to the left side of the ballast (1st photo), i.e. the side with the jumper between the terminals. That will bypass your key switch (hot wire the car). To do this, stuff a bare wire in either terminal or get a fancy piggy-back spade. Don't leave 12 V on long, just for testing. Too long and it can overheat your ECU or coil. Overnight and it will discharge your battery.