@userc2 start of by following the Apple flowsheet which goes like this:
Screen is blank; backlight isn’t on; computer doesn’t respond
1 Reset the computer by holding the Command-Control-power button simultaneously.
2 Reset the power manager by pressing the reset button above the power button. Wait five seconds and press the power button. Note: Before continuing, make sure the reset button is not caught under the plastic of the top case.
3 Check power adapter cable.
4 Try known–good, charged battery.
5 Try known-good power adapter.
6 Reset PRAM. Press the power button, then hold down the Option-Command-P-R keys until you hear the startup chime at least one additional time after the initial startup chime.
7 Check inverter and display cable connections to the logic board.
8 Remove keyboard and additional memory (if installed) and restart computer.
9 Replace logic board.
Now, don’t replace the board yet ;-)
This “because it has been dead for a very long time, and the computer won’t charge it “ could just be one of your bigger issues. Remove the battery and check the contacts etc. After that you want to do a deep dive and take a look at the charging board as well as the DC-in board. Use these guides to work on it iBook G3 Clamshell Repair and remember to always post good clear pictures with your QUESTION as you take things apart and have further questions or problems.
Adding images to an existing question
The part you definitely want to have a real good look at is the charger board. It should contain the PMU99 which is actually a Mitsubishi IC and its function includes :
controlling the sleep and power on and off sequences
real time clock
controlling power to the other ICs
monitoring the battery charge level
controlling battery charging
supporting the interface to the built-in keyboard
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