Ok. Try booting it into test mode if you can, do a rom test and see if any of them are bad.
I'd check both the naomi and the cart rom tests, provided you can get to them.
Also, according to another post on the naomi board posted above, the naomi hardware is also sensitive at the 3.3 voltage, so check on that as well. I'd recommend checking at the board and not the power supply.
Check for board damage as in this link ...
http://www.ki4swy.org/repair/2010_07_NAOMI/A leaky or bad cap could result in what you're describing.
Another possibility is loose or damaged wiring. Sometimes there's a break inside the insulation so it's not visible, and when it's cool it has continuity, but when it heats up, it will separate. Those are frustrating to try to find.
I'd also take a look at the molex connections from the power supply to the board. Make sure they're not loose.
I can't stand having a game down all weekend, I'm sure it's frustrating for you.