I have an old iBook G4 (A1054, 1.2 GHz) which has issues when it loses power or is shut off. If the battery drains—which happens quickly, as its remaining capacity is very low—it enters some sort of weird mode where it's not really awake (the screen is black, can't do anything) but it has no pulsing light indicating it's asleep either. The only way to exit this mode is to hold down the power button for ten seconds until it shuts off, and attempt rebooting it.

Almost always, however, it makes the sound of the optical drive starting up, and then doesn't continue past that point. The screen doesn't come on, and things like resetting PRAM don't work. Occasionally a fan comes on loudly for a second or two. This sometimes seems to correspond with my pressing down on the rear-right casing, above the power jack.

In the past, shutting it off, disconnecting it from power, removing the battery and waiting for 30 minutes would do the trick, but this time I have done that several times, letting it sit for up to several hours before retrying, to no avail.

Any ideas?