PowerBooks have an internal backup battery, or "PRAM," battery that, when dead, creates power management issues. AS these computers are now at least 13 years old, none can be expected to have a healthy PRAM battery. The sad issue is that new PRAM batteries have not been available for a very long time. The only newly manufactured backup batteries appear to be for only the 17-inch 1.67ghz models. Some people sell used batteries but, as all have the same issues, this seems about as useless as buying used chewing gum. Also the changeout is a fairly major teardown.
I found that, when the PRAM battery is old, one needs a fully charged and healthy main battery to get a boot, even with the power adaptor connected and active. If both the main battery and the backup are dead or not working properly, PBG4s are hard to get started.
An old tip someone gave me that may breathe a little life into the PRAM battery is to remove the main battery and leave the computer off AND connected to wall power for about 48 hours. The PRAM battery rechargeable so, if the insides are not completely fried, that time on power may pump a twinkle of life into it. No guarantees but worth a try.