So, presuming that your set up is similar to the way i've got mine connect, except that I've got a combined modem router device. Which is then connected via an ethernet NIC.
You'd need to know what system your isp uses i.e. static or dynamic address.
All I have to do is to boot the knoppix disc, then when you've got the desktop up and running, you should have a knoppix icon on the taskbar, I normally click that and select configure network.
A window open's and i just apply my LAN setting's and you'd have to select whether it's static or dynamic (i.e. your provider uses "DHCP" whereby the system would know to query the provider for the IP address).
then I can normally browse ok.
hope that help's
p.s. you could alway's check this site