27" Thunderbolt Monitor black screen but otherwise working. Repair options?

I've had the problem that a LOT of people have had with the Thunderbolt Monitor - black screen, nothing will wake it back up, but it will randomly work. Meanwhile, everything else on it works perfectly. I'm going to bite the bullet and buy either a replacement Power Supply board (which includes the Thunderbolt board), or the Logic Board. My question is - which is responsible for this problem? It feels to me like a Power Supply problem, but if anyone else has experience with a successful fix, it looks like there's hundreds of people who'd like to know.