I've read the various problems/ resolutions suggested here; I think mine is a bit different.
The screen may/maynot initially come on, but perhaps not as bright as 'normal'. This happened suddenly, resolved for a very short time after rebooting, would come on, only infrequently, and for variable amount of time. I tried the solution Nanna suggested; the screen lit up, faintly and briefly (we're talking a few seconds) before a return to black. What I've noticed is - the screen, dimly lit, goes out immediately when I open the lid past, say, 30 degrees.
The computer seems to work with an external monitor, though on occasion the screen will go black for a few seconds, and on without intervention. I have other, software issues, and my keyboard has sticky numerical keys.
So.... Ccfl tube? magnetic switch? Inverter? short in my cable? Is there a cure, or should I have a viking funeral?