Several of the Console utility crash logs should point to some aspects of this issue.
With a known good battery of less a few years age, and other parts of working status
you could troubleshoot by simply trying others in place of original or older ones.
If the battery and the AC adapter could be proven OK, then the third item to consider
in hardware, would be the DC-in board. - A fourth worth considering, is a PRAM battery.
If your model PowerBook uses a separate clock battery that is on or near the logic
board, that may have stopped holding a charge and may need replaced. A few models
of PowerBook did not use a separate clock battery, when this goes dead there can be
startup issues. This may also affect other aspects of the computer. However should
the main battery be old (does not necessarily mean a high charge/recharge cycle #)
it may need replaced regardless of the status of the clock battery.
You could see what exact version of repair guide at iFixit.com for PowerBookG4 and
that may show you how to replace the clock battery. There is a fair chance that needs
a new one, and could likely also need a main battery. They usually don't last very long.
When you identify the correct exact PowerBook model series you have, then the parts
to fit it should be also readily identifiable. Some may be harder to find, going forward.
Where the clock or PRAM battery is concerned, some users were able to disconnect
it from the logic board, and use commands to reset the PRAM (and/or also PMU) to
get their computer to boot up again. While this workaround could make it work, this
would not repair the issue and a new clock battery would need to be installed.
Not sure how helpful this info is...
Good luck & happy computing! 🙂
