Sounds like the DC Input board problem that used to kill G3 Powerbooks. Not saying that is what it is, but the symptoms are similar.
There is a very tight configuration of "cables" (flexible printed circuits etc) in the top right corner that is where the DC comes in and the screen gets power. I had the "disappearing screen" repaired under warranty that involved also replacing the logic board as the tech wanted to ensure that the problem would not reoccur.
cPanelฎ has some teardowns, but be warned opening iBooks is not for the ill-experienced or faint hearted.
Fixit Guide - DIY PowerBook, MacBook, & iBook Repair & Disassembly
Given the flickering orange/green suggests it could be the plug, but as you suggest its only under battery power the battery may not be seated correctly or completely dead.
If you could swap with a known working battery that would at least narrow it down some more.
Hope that helps