The basics are that Knoppix does a DHCP handshake with the router at boot time and you are on the network when you boot.

The only router that I have had this fail on was an old Belkin 802.11b router. It would not handshake properly with Knoppix (apparently was only tested with Windows). But a newer Belkin 802.11g and many other routers all worked fine for me. Are you sure that you are not on the network? What is the output of ifconfig?