For me it was a problem with the laptop not coming out of hibernation properly and completely freezing, the only option was to power off. On reboot nothing would happen, the screen would not even be initialised so it is nothing to do with the screen.
As the solution is to remove the power lead, remove the battery and hold down the power button it would seem to be an issue with the laptop retaining some residual charge which is preventing the laptop from booting. I've heard of other poeple who have managed to fix this by simply letting the battery run out and then leave it overnight, this will again dissipate any residual charge but is just a much slower way of doing it. Holding the power button down with no power sources attached will dissipate this charge and allow the laptop to boot when a power source is reattached. Unfortunately if the laptop boots and the screen is blank then it is a different issue, if the image on the screen is faint it is most likely a problem with the backlight and in these instances this fix will not work.