I thing you are very lucky that your iBook G4 has lasted this long.
This model was /is notorious for having bad solder joints on the graphics chip which would cause the display to throw all sorts of video images, everything except a picture, and would also cause the machine to not boot.
Hello there--
Been struggling for months about how to fix this issue. I own an iBook
G4 (OS X 10.4.1 Tiger) as of 2005 or so that has worked perfectly
since. I also own this MacBook which I am using to write this plea for
assistance, but use the iBook as a computer for all of my quirky gaming
crap. Anyways, it's still a very important device to me. Back to the
point...
I have dropped my iBook G4 off of my bed a couple of times as it slides
off of my lap, but has worked 100% fine after, except for immediatley
following the most recent drop. The first time I dropped it, it fell
about 1 foot onto my hardwood floor. It landed on its side as the
notebook moniter was at a 90 degree angle. This caused a crack in the
upper-right hand corner in the [only] the plastic and the iBook still
worked fine. I dropped it a second time while playing a fullscreen game
in the same scenario off of my bed, and the screen turned blank white.
Let me set this straight: It appears that MOST all of the computer is
working fine (still hear startup noises, battery works, powers up, etc.)
But here's where it goes wrong:
I start up the iBook G4, hear that famous Apple chime, the screen
backlight comes on, and I am left with nothing but a blank whitish
grayish screen! No Apple logo or anything that I can see. No sunburst
loading circle. Nothing but a blank white screen. The volume can still
be adjusted (makes the squishing noises) but the brightness cannot. I am
assuming that something got unconfortably jumbled or disconnected in
the iBook during that last fall. I have heard that it may have something
to do with a LVDS connector cable or something. The backlight DOES
still work, there is just no icons, words, etc. on the screen; just
blank white light.
Due to my cat-like curiosity and strong desire to get this thing fixed, I
attempted part dissassembly without know exactly what I was looking to
fix. I got overwhelemed and will soon be re-assembling the device until
someone can confidently tell me what I need to get in there and do! I
I have suspicion that it is the LVDS cable needing a bump or nudge into a
socket of some sort, but I have no proof to base this on other than
reading about semi-similar problems on the Internet.
However, in related problems, usually their screen is black. Mine is
white. I am not in a financial place to be spending any $$$ on a new
cable, part, etc. but I do believe that this problem is self-fixable for
free.
Issue Overview after drop:
-Notebook powers up + chimes
-Screen light comes on, but stays at a blank white screen
-Sound volume works, brightness does not
Please PM me or reply to this thread with any details, advice,
resources, tutorials, photos, etc. ANY and ALL is greatly appreciated.
Thank you all in advance,
Sam

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic