It certainly looks like your hardware on eth2 is connected and got a proper DHCP setup, although why you seem to have a eth0 and eth2 but not eth1 isn't clear. Once again I'm wondering if you are not really connecting just fine but don't realize it, in the past some people have thought they were not conneced when indeed they were. Alternately, it might be an ip6 vs ip4 issue, I can't rule that out but I see no sign it is. Another fix for ip6 problems tends to be to change dns servers.

You ping an ip address or url by typing ping and the address at a shell prompt, as in ping www.knoppix.net or ping 72.36.188.40

You should also try accessing the knoppix.net site by both the above url and the above ip address. If the ip address works but the url does niot then it is a DNS issue.