73 Duster Electrical Issue

Your post does not make sense, entirely. You say "it won't turn over at all" which implies that the starter won't crank, is that correct?

But then it seems you are messing with the ballast and ECU, etc, which has nothing to do with getting the engine to crank??

Please clarify.............

IF IT WILL NOT CRANK.............Is this a stick or automatic and if stick, do you have a clutch safety switch?

If it cranks but no spark that is another matter.................Also, the "run" line GOES COLD if you twist the key to "start." That is NORMAL. The coil / ECU power during starting comes from a separate contact on the ignition switch, known as IGN2, during "start."

What do you mean by "HEI distributor" EXACTLY?

If you have such as that, you might not need nor want a ballast, and what about the ECU? You referring to Mopar ECU? Should not need that either, with an HEI setup