You should be able to connect through eth1. In fact it will be a lot simpler getting the wired link working than the wireless one.

What people need to know to be able to help you is what you are connecting to. For example, if you are connecting to a router with DHCP services, Knoppix should have been able to get all it's configuration information from that and would just be up and running. If no DHCP sever is available then you might have to run netcardconfig and manually input the rquired information (which you may need to get from the service provider). If you are running on a DSL connection without a router then you may need to run PPPoE software to send the right type packets to your DSL provider and to log in (bad idea to run DSL without a router though, get a cheap router). So try any of the above if they apply or tell people what you're trying to jack into.