The 300 Mhz Blueberry is an extremely difficult Mac to upgrade to Mac OS X for these particular reasons:
1. Boot size partition size limitation if you upgrade the hard drive:
http://docs.info.apple.com/article.html?artnum=106235
This means some applications won't install because you have to separate where their data files is stored to a separate partition if you install a larger hard drive. With Mac OS X, 2 GB minimum of your hard drive is used up to begin with, and it has been arbitrarily found to need at least 15% of the hard drive free to run smoothly.
2. No Firewire, meaning any backup has to be done over USB 1.1, typically to CD burner or hard drive, but recognizing that USB 1.1 is only 12 Mbps at max speed. This also will prevent you from installing 10.4 or later unless you use
http://www.macsales.com/ 's XPostfacto. But given the official RAM limit being at 256 MB + 32 MB or 64 MB (whatever your onboard RAM is would be added to that), 10.4 will barely have enough to run word processing and iTunes, and a few small games. Dashboard widgets are out of the picture.
3. No ability to boot off external hard drive or CD drive, to test the quality of your backup.
If the battery fails to charge, it could be indicative that the clock capacitor on the logicboard or the power supply has broken, and needs repair from one of these vendors, or the battery itself just needs to be re energized:
http://www.dttservice.com/
http://www.powerbookresq.com/
http://www.microdocusa.com/
http://www.macspecialist.com/
http://www.techrestore.com
To check if the firmware was updated, run the firmware update again from:
http://docs.info.apple.com/article.html?artnum=86117
for your iBook once you are certain your clock capacitor is happy. There is no "clock battery" unlike other Mac models, and installing the firmware when the capacitor or battery is broken, could permanently break your machine.
If you are willing to put together this house of cards, by all means do so. But unless your Mac has Firewire, I wouldn't really bother.