Even though the RAM tested out as fine, I wouldn't completely rule it out. If there are multiple sticks, pull one out (or all except 1 or 2 if you have 4 sticks) and see if the problem persists. If it does, obviously try it again with only the other stick seated.
My other thought would also be the PSU. If you can't get to the voltage rail readings in BIOS, you'd have to measure it with a DMM.
Since it won't even get to BIOS, I would almost rule out the HDD. The mobo could be a possibility, but it's really hard to diagnose it as such if there isn't any obvious cap damage.
In cases like this, it's easier to find somebody with a working PC and start swapping in/out parts until you narrow down the culprit.