Hello and welcome to the support community.
First of all, routers are not accepted in your household? So how do you get online?
In order to use broadband Internet you need a router.
You iBook would have been supplied with the following items when it was new.
1. Power Adapter
2. Power Cord
2. Modem Lead (While telephone lead used for dial-up Internet via a phone line)
3. VGA adapter to allow an external screen to be used.
No USB lead were supplied and the only battery supplied with your iBook would be that attached to the bottom of the iBook. (White)
A USB lead could have been supplied with other devices like printers, scanners, cameras or phones.
There are four ways you can get online with your iBook G4
1. Connection via Ethernet to a router.
3. Wireless via installed Airport Card to a wireless router
4. Dial-up modem (What the white phone lead is for)
6. USB 3G dongle (Or connection using a cell/mobile phone that's compatible)
I hope this helps