I noticed this forum has a lot of posts about iBooks (white) with screen issues. Specifically, the "I can open it to 30 degrees but beyond that it blanks out" variety. Your local Apple repair person would offer to replace the sreen, which works, but costs $$$ (I got quotes from $300 to $600, including parts and labor).
Good news: this is a WELL DESCRIBED problem with the ibooks. The cable that runs to the screen from the motherboard takes a tortuous route through the hinge mechanism. Over years, the wires in the bundle can snap clean in half from all the flexing/stretching with repeated screen opening/closing.
It's described in number of places:
http://www.schwarztech.us/reviews/schwa ... able.shtml
http://p197.ezboard.com/fmacnightowlmes ... D=58.topic
http://engineroom.blogdrive.com/archive ... 3_o-0.html
The fix is to replace the "Inverter Cable with Reed Switch", available from Powerbookmedic.com for about $50 bucks.
ONE KEY DISTINCTION: the problem I'm describing only effects the iBook backlight, not the LCD screen itself. "How can you tell if it's the backlight?" you ask. Do this experiment: take a flashlight and shine it through the translucent Apple logo from the back of the screen. Can you see the LCD image on the screen? Then it's the backlight.
You'll also need the Torx T6 and T8 tools (about $8 each) to take out the little screws on the case and screen. You also need time...and lots of patience. It took me, from start to finish, about 5 hours. The sites above do a much better job of explaining it than I can.
Some advice if you attempt to tackle this:
1) Get the ibook repair manual.
2) Get some empty ice trays to categorize/store the screws. There are tons of screws in the various disassembly steps - they're of varying sizes/lengths. It's easy to get them mixed up.
3) Keep a paper diary as you do each step: write down things like "remove 2 short screws from battery bay" with a note to yourself about where in the ice tray you put the tiny parts.
I did it, saved more than $400. The folks at Powerbookmedic sent the parts in 2-3 days. Worked like a charm...