I don't think (for once) that the PSU would be the issue here, as these are newer boards that pull most of their power from the 12V rail rather than the 5V or 3.3V rails. Thus, a PSU with a strong 5V & 3.3V rail is not really needed. If you suspect the PSU, put it in another more modern PC (preferably something with a higher-power CPU or a mid-range-y GPU) and see if POSTs there. If PSU passes that, it's more than likely OK. It's an EVGA PSU, so pretty decent and not some no-name gutless wonder.
Now, only other thing I can think of is if this particular PSU you have perhaps has either a faulty or too quick or too slow of a PG (power good) signal and/or if these two motherboard are picky with the PG signal for whatever reason.
But all in all, I'm leaning either towards the problem being somewhere else with the rest of the hardware (i.e. are the CPUs and RAM on these boards known to be compatible with them) or perhaps user error (do you have the 12V CPU connector plugged in?) I know the latter seems like a silly mistake that no one should make... yet, I've done it a few times myself, despite years worth of troubleshooting PCs.
Oh, and one last bit: are you using a dedicated GPU to test these boards or the onboard / IGP (if equipped)? If it's the former, perhaps try another GPU, just to be sure the one you have isn't too new and/or somehow incompatible with these boards. Case in point, some new PCI-E gen 3.0 and newer GPUs may not reliably POST on older boards. And sometimes, even gen 2 PCI-E can be a problem for get 1 boards.
Last but not least, make sure you have a known good CR2032 battery in each board before testing it. I've had a good deal of boards refuse to POST with a dead or missing CMOS battery. Ditch the POST card too, at least for now, and give the boards a good wait (10-15 seconds after power-up) to see if anything happens. Although I don't recall a POST card to ever make a system hang, I still like to think that it is possible.
