Computer continuously power-cycling
Solution 1:
Just by looking at your trouble-shooting steps it looks like a MoBo issue. It's the only constant in all of the different things you have tried. There is probably a short somewhere, bad solder, or a faulty power connector on the MoBo. I'd try swapping it out and keeping everything else the same, see if that fixes the issue.
It especially seems apparent that the MoBo is the issue because you say that a number of people with the same or similar MoBo are having the same problem. So that is likely your point of failure.