Okay well after a bunch of thought, I have decided to share the fix with you all. I am surprised after so many years nobody else figured it out.
I shared it with member "Evolutionoftime25" first on his assurance he would keep it quiet so I could spend the day thinking of a way to make money from this fix; since I program and sell used PCMs for a living. However, in the end, I just decided to share it with you all rather than having you send me your PCM for me to open and modify.
The problem is not with any HPTuner device. Nor is it a problem with the PCM; neither software nor hardware. Yes, that is correct, it is neither a hardware or software issue with the PCM.
The problem is actually with the wiring of the cars. You can see that there should be two switched power wires coming from the ignition switch. One on Pin 11 and one on Pin 12 as seen in the picture below for a 2004 SRT4.
2004_SRT4_pcm_plug2.jpg
However, here is a picture of a 2004 SRT4 PCM Plug. Forum user Evolutionoftime25 was kind enough to verify my fix and to send me this picture. We can see the Dark Blue with red stripe wire is present in Cavity/Pin 11, but there is nothing in Cavity 12.
2004_SRT4_pcm_plug1.jpg
This missing wire is why the early 2004 PCMs across the entire Chrysler lineup fail to write. I speculate some bean counter must have decided that it was safe to remove this seemingly redundant wire to save some money. Perhaps 2 feet of wire multiplied by 1 million vehicles, is 2 million feet of wire and a lot of money for that copper. This was a giant error by someone! Chrysler couldn't even flash their own updates! Their fix was to make all of their later PCMs work with the single "key on" wire in pin 11, rather than change out a million wiring harnesses to include the missing wire in Pin/cavity 12. Replacing PCMs was the cheaper option.
If you add this wire and join it with the wire in Pin/cavity 11, your problems will be solved. For those of you that flash on the benchtop, as I do, add this wire to your harness too. You can add the wire like I have demonstrated here:
2004_SRT4_pcm_plug3.jpg
Yes, I know my repair was sloppy. It was a proof of concept repair picture and I am sure I could have made it nicer. It works, and that is the main point. Enjoy all!