If your newer internet router base station does not have backward compatibility with the earlier wireless protocol - of an older (colors G3?) iBook, and the USB port too slow to use a modern adapter (no drivers?) to wi-fi, you could see about using an ethernet cable to the base station, if it has a port.
For a browser, depending on the Mac OS installed in the old iBook, you could try iCab - all the way back to an older OS 8.6 - or so. And with varying results. They have newer versions in the main page, older via page link. A few browser builds have 'older version' download pages for some stable but unsupported ones in archive.
And if you can find an old AirPort base station, perhaps an Extreme orb or the first models Express, those should be backward compatible or near the exact vintage to be happy in shared antiquity with the iBook.
Which iBook model is it? White G3 or Colors? You could run the serial number in a lookup page, or go through & match the specs if you have the Mactracker application.
Good luck & happy computing! 🙂
{PS: Not sure if a replacement battery of quality is available or worth the cost}