Well, you are getting an IP address set up by DHCP, so we know that you network interface works with Knoppix and that you can talk to the router. The data looks valid also.

I'm not sure why you can't get the browser working. There has been some discussion here about problems some people have had with IPv6 vs. IPv4 where the IPv6 wasn't working quite right. My ISP isn't supporting IPv6 at all (as far as I know) so I have not run into this myself, but if I remember right (and I frequently don't) they had found some configuration setting in Firefox to disable IPv6 and that resolved the issue. The only other thing other than looking for such a setting that I can suggest that may tell you more is to try the following test:
in a console ping 67.212.237.18
if that works, ping knoppix.net
If the first ping works and the second ping fails you have a DNS issue. Maybe the DNS didn't get set correctly by the DHCP, and perhaps you could run netcardconfig and correct it. If both pings get responses then you have Internet connectivity and just have a browser issue. netcardconfig might even correct that if you point to a differnt DNS server without IPv6 support (this is, of course, all just theory).

Please report back what you learn.