Hmm sounds like either the Power Management Unit may be failing or your power adapter simply isn't making constant contact.
I would see if you can find someone with a similar iBook at a coffee shop or something (or go into an Apple Store) and ask if you can plug their power adapter in for a few minutes. If it stays amber while plugged into their adapter, you simply need a new one.
Another thing you can try is to reset the NVRAM then the PMU. Here are the steps:
1) Shutdown computer (not restart)
2) Press the power button to turn on computer but immediately hold down the OPTION + COMMAND (apple) + O + F keys (as in Oscar, Frank). Continue holding down until you get a white screen with black text.
3) At the prompt type "reset-nvram" and press return (don't type quotes) The prompt should say "ok" nearly instantly.
4) Type "set-defaults" at the prompt and press return. Again it should say "ok" after.
5) Type "reset-all" at the prompt and press return. Your computer should reboot.
That's how you reset the NVRAM and return it to default settings. To reset the PMU, follow the instructions on Apple's site:
http://docs.info.apple.com/article.html?artnum=14449