Why is my iMac turning off 20 seconds after boot?

The iMac turns off after 20-25 seconds. So here is a detailed list of what I have done so far:

• I have replaced the power supply, logic board, DC-in cable, PRAM battery, RAM and HDD.
• I have run every test that I have read about and it still shuts off during any test at the 20-25 second mark.
• All 4 of the LEDs turn on during boot.
• I can get the apple logo to appear, I can start a hardware test, and even boot into single disk mode.
• I even went as far as removing the optical drive in case it would cause an issue on boot.

When it boots up and make the tone at the 20-25 second mark everything shuts off even the LEDs from that point it will not power up until you removed the power cord for 15 seconds then plug back in. That’s the only way to get power restored to run additional tests.

Any assistance would be greatly appreciated. I have uploaded a video that shows from power on to the point it shuts off.

What I can say about the logic board is that this same issue was happening before I replaced the logic board. Which led to the replacement of each other piece of hardware.

Do you think its a coincidence that the old and new logic boards could be presenting the same issue?

I will also try and find schematics to troubleshoot as you suggest.

Thanks again and any other ideas would be much appreciated.