After reading this thread, I came up with a longshot way to solve what seemed to be a bad logic board; I intentionally overheated the computer, while turned upside down.
My MBP 15 A1226 had signs of a bad logic board - the hard disk would sound on, the fan would start up, the MagSafe power indicator light was on, but the computer's 'power indicator light' (the one that normally pulsates when the comp's sleeping) would light up and glow steady, and the screen would remain completely dark and unlit. I tried suggested steps from iFixit, Apple, and macrumors (resetting PRAM, SMC, etc.) and there was no change in the computer's symptoms. This lasted a day.
What seems to have resolved it was this; plugged in the AC power, turned on the computer, closed it, turned it over, then put a folded-up quilt on top of it, and went downstairs and watched Pineapple Express. When I came back to it, I opened it, unplugged it, then turned it off. The power button was extremely hot and the fan was blowing very high. I held it in front of a fan and about a minute later pressed the power button and it booted up like normal.