Am I to understand that the network interface is on a PCI-E card and not on the motherboard? That seems strange, particularly for a recent Asus board. I'm thinking that maybe the interface is on the motherboard, even though you called it PCI-E above (maybe a terminology that Asus uses). Obviously with that BIOS date it's a pretty new motherboard. While Knoppix is doing better in supporting 10/100/1000 NICS, it might be that it's just too new to be supported yet, even though it's being recognized. That's just speculation, but is seems to fit with everything that you are reporting.

My first though is that it seems from your previous posts that you very well may have another NIC available. If so I would try adding that NIC, hopefully a simple 10/100 NIC on a PCI interface. If there is a BIOS feature or motherboard jumper to disable the other NIC and you want to really keep things simple I would disable it, and if it is a PCI-E card I would remove it. You should still be able to get the add-in NIC working if you don't, but this would prevent problems differentiating between eth0 and eth1, and help be sure that DHCP at boot time tried the NIC that you wanted it to use. Of course, feel free to try experimenting without disabling or removing the 10/100/1000 NIC if you wish.

I expect that that will resolve it for you. Hopefully a future release of Knoppix will suport your newer hardware.