Well,
As far as i'm aware, you would be eligible to take your Ibook back to the store and get it fixed as many times as you like. If you're under warrenty then I think you should have no problem. Try an Apple Store.
If you take your Ibook back to the store and they fix it more that 3 times, they should give you a brand new one. REMIND THEM when it get's close to or on 3 times.
I assume it's an Ibook G4.
I hope my Ibook doesn't go this way.
Out of interest, where do you pick the Ibook up from? E.g The left hand corner by the trackpad, by the CD-ROM drive? I'm not sure but I think npicking it up continuously from a certain place may put strain on the graphics chip and slightly dislodge it.
Apple really need to realise that these Ibook's have a design flaw with the logic board, and the screen cables.
I know this is probably a logic board problem, but if you can get it to boot up, do a backup pronto. If apple replace your system then it's bye bye hard drive.
Any more info required or i've missed anything just ask,
Sean