After having a problem with my screen (it would sometimes work fine, then flash and go black, and sometimes not work at all) I took it to the local Mac reseller, who said it would probably be the cord between the screen and the computer. 5 Days later, I rang them, and they said there was nothing wrong with the computer, and that I can come and pick it up. Went to pick it up, they turned it on and nothing happened. Not even the happy little mac chime. Also, the #1 key was now ripped out of its socket. . Will not be going back there.
Now the cord problem has gone from a $100 problem, to a $2000 logic board and screen replacement problem! I've been sent quotes for these, but I really don't think it's the screen, as the screen sometimes works fine. The computer sometimes boots up now, but only if I have it on certain angles, on a hard surface. Before I gave it to them, it would always turn on, just with no screen sometimes.

Any thoughts on what else the problem could be?

maybe they took it apart and didn't connect it all back together again? have you tried connect it to an external display? because maybe the screen and sound connectors have been disconnected from the logic board but the computer may still work.
But i guess even then...
Humm take it back and tell them you made my computer worse then before..

like the iBook G3's, the G4's sometimes had a logicboard problem.The Apple Centre is not entirely wrong.See here...
http://www.coreyarnold.org/ibook/ and here...
http://www.applefritter.com/node/10193
Stewie

Edit:
Note your iBook may have been part of the recall list. Go to Apples site and compare your serial No. as part of that program. It may be a moot point as you are probably too late to participate in that recall however. Search the site here for threads in a similar vein.

Also just Google for " iBook G4 Logicboard fix " and that will throw up more links and helpful to your problem.
Stewie

is this related to your problem?

http://www.reghardware.co.uk/2007/09...g4_in_denmark/

a wedge under a particular logic board chip in my ibook G4 and its been working beautifully after the dead logic board incident of 2006