Yes, the problem you are describing is very common. You need to order Apple Part #922-5017 (Inverter Cable with Reed Switch) that is sold at various online locations for around $55.00 or so.
Go to Apple's discussion boards and you'll find that there are hundreds of people that have this problem. The wire assembly that runs from the logic board to the screen (backlight, LCD, etc.) has around six or seven wires in it. Due to poor industrial design, there is no slack or any other measure that was constructed to prevent breakage. Normally, it is the black wire that has severed, yet from a visual inspection it "looks fine" - but in fact breaks WITHIN its insulation. Replacing the part and than keeping opening & closing to a minimum is a good solution.
Otherwise, if you're feeling a bit brave, you can solder/jumper in a new piece on the black wire. It's VERY tight working in there but many folks have repaired it this way. When you do this repair, make sure that you choose a wire that has a LOT more strands than the existing black wire (a 7-strand wire).
I just got an iBook in superb shape for a great price due to this defect. It doesn't bother me at all because I knew of it when I made the deal. I'm a bit nervous about attacking the problem, but the discussion boards are incredible sources of help. Here's a link to the discussion: http://discussions.info.apple.com/webx? ... 9748b6/144