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Once driven and sitting (warm) it turns over but will not start under load (key all the way forward).

Will occasionally start when you let off the key, on that last turn of the engine.
While having this issue it will consistently start with key forward and jumped from starter relay
.

I agree with several, but Budar's suggested follow up test is the most logical next step.

Budar wrote:
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Have you used a test light to verify power on the brown wire when the key is turned to START?
Pull the yellow wire off the starter relay while you test.
This will prevent the starter from engaging.
When it acts up, test the brown wire. That wire should power the ignition during START
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Just to make this clear.
The 'brown wire' is the one that gets power when the key is in Start. The service manual shows this as "Ignition 2"
It goes from the key switch through the bulkhead connector to the ballast resistor(s) to the coil.

"Yellow Wire" to the relay also gets power when the key is in Start.
Schematic attached to post.

So the test procedure suggested is this:
Remove the yellow start wire at the relay.
Then connect a test light to the brown wire connection at ballast resistor.
Or, maybe better, back probe that connections with a voltmeter. Other lead of voltmeter connect to ground.
With key in start position voltmeter should show battery voltage. To know what battery voltage is during start you must measure it at the battery with key in start.
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I have replaced the following with NEW parts:
Complete dash harness
Both engine compartment wiring harnesses
ECM
voltage regulator
starter relay
ballast resistor
coil
cleaned all grounds

I have a new, in the box ignition switch which I can plug in and turn the car but it still won't start.

I have not replaced the distributor.

Maybe I'm just ignorant on the T/As, but based on what I know, the ECM and distributor are modifications. Therefore, I am assuming this is single ballast resistor set up and a 4 wire ECU harness. Is this correct?
Phillyrag asked the same question, but he assumed it was a dual ballast harness.

This could be important to the follow-up steps to the diagnoses if there is full power available at the brown Ignition 2 wire during start.

Just because stuff is new doesn't mean its good or correct. I trust genuine old stuff more than most new stuff (sad).

First schematic is typical stock setup for '70. Little details will vary from year to year and model to model. For example 'Run' wire may go to VR before ballast.
Second one is a common arrangement when a magnetic pickup distributor and Chrysler type ECU is added.






Charging-diagram70.pngCharging-diagram70-withECU.png