Youi do have a router. The IP address that you are showing is a private IP address. There are sets of ddresses set aside for this, the 10.xxx.xxx.xxx group (used by large organizations and some home routers) the 192.168/xxx.xxx group (used by most home routers) and the group 172.16.0.0 - 172.31.255.255 which your router is using.

Why you are having problems isn't clear. Try accessing the 172.17.0.1 asddress and see if you see setup information. Try to ping knoppix.net and then try to ping 216.32.81.146 (if you can ping by IP address but not by the URL then it's a DNS issue, as both go to the same system). Also, if your router has any features that would limit traffic by MAC address or any similar rule, turn these off and try again. And some times people report that just cycling power on a router will correct a problem like this.

At first glance I can't see what's wrong; the information you printed out seems to show that Knoppix likes yiour network card and that the NIC did do a DHCP handshake with the router.