I had the same problem, it was hardware related though.
There are two little metal contacts that ground the battery cover, well one of them slipped though a little and was shorting pins on the motherboard. So fortunately nothing blew and it just was not turned on.
So obviously there is some form of protection from shorts that it will not power on.
Anyway check if it will turn on if only the motherboard, LCD and battery is plugged, without housing or anything else. Be sure that the back of the battery does not get into contact with the MB if you are going to try.
Good luck, hope you get it fixed..