Quick fixes for that scenario would be something not seated well, but ive seen plenty of bad mobo's that work perfect every few reboots. As far as possible problems your looking at just about anything hardware related from improperly seated RAM, bad wall socket, bad motherboard, OC'ing, failing GPU, issue with monitor or cable, Power supply issue, anything.
The methodology ive found that works best is to removed parts / switch around / replace, to determine the cause. But being an intermittent issue like your having, it may never be certain that whatever you just did (say replace RAM) actually fixed the issue, only time will tell.
I would run memtest, re-seat everything, check the board for blown caps, check the PSU for blown caps. And hope its just a seating issue.