Could be the cable to the display from the logic board is worn; or weak.
There are a few other parts in support of that function which can go bad.
A data cable or wire could be at fault, as that would not affect the power
to the display from the logic board or other connection from the body of
the computer; so the unit may need to have a professional inspection.
As an older unit, finding willing repair & diagnostic help may be difficult now.
Some shops specialize in a wider range of Apple portables and so may be
able to get parts & have skilled technicians who have experience with those.
If none are available locally, then one may have to look further away and
use a parcel service or a post office flat-rate padded box to ship to service.
Depending on where you are located (country/region) options may vary.
•Resetting PowerBook and iBook Power Management Unit (PMU)
A power management unit reset may be an exercise to perform
yet it may not change the symptom if the parts have failed.
Sorry to not have so many ideas of a helpful nature to fix your ibook.
Good luck & happy computing! 🙂
