The router is a Virgin Media, Netgear VMGD 280 model and will be set for WPA2 according to the device documentation but it is not a subject I know about
OK, that's what I needed to know. I'm going to make an educated guess here, because 10.3 is quite old now and it's not a version that I've ever used, but I'd venture to say that the driver for the wireless adapter built into your G4 iBook probably doesn't support WPA2, which is a relatively new wireless encryption standard. It certainly would post-date the last update to 10.3 at the very least.
This puts you into quite the conundrum because you really do want to use WPA2 encryption where available, but it's probably not practical to upgrade to 10.4 or 10.5 with a machine of that vintage.
I would say that if you really must use the iBook wirelessly, your best option would be to log into the router and change the encryption to WPA (as opposed to WPA2) and see if it works with it. This will degrade your network's security slightly, but for the most part, WPA is perfectly viable even today.
The specific process for making this change is going to vary from wireless router to wireless router. Hopefully your router came with some documentation (it may have been including electronically on the CD that came with it). Generally the process will be to connect to the router by visiting a special webpage, logging in and finding the wireless security settings to change and subsequently save the changes. Then, you'll need to reconnect to the router on each computer that uses it wirelessly.