You might want to tell us all of the settings that you made with netcardconfig.

I understand that you have static IP addresses on all of the other systems (and I understand why, even though this is a pain, that you would want to do this with an SMC router). However, even if all other devices have static IP settings, the router can still run DHCP (just make sure that the range of addresses that it hands out does not contain any of the static addresses. Let it hand out 220 to 230 for example). If you do that can Knoppix connect to it, configure with DHCP and talk normally? (Yes, you may still want to give it a static setting, but this test should tell us a lot and looking at the configuration might show what is configured differently.)

It sure doesn't make any sense that you could ping other boxes on the local network but not the SMC router. Can you ping other computers plugged into different router ports, or can you only ping computers that share the switch before the router? Have you tried plugging the Knoppix box right into a router port to take the switch out of the picture (not that I can imagine anything the switch could be doing wrong in this case)?