try this.
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That didn't work, but it seems like it's just from my not understanding.

When I tried using a DHCP broadcast from eth0 or eth1, it would simply say 'Operation Failed'. This confuses me because I have DHCP turned on in my router settings.

I tried doing it manually, but it doesn't seem to like me. I figure this is because I'm using the wrong IP addresses in the wrong places.

Information it's asking for:

IP Address for eth0
Network MMask for eth0
Broadcast Address for eth0
Default Gateway
Nameserver

Information I have:

Router IP Address
Router Subnet Mask
Network Address Server Settings (DHCP) Starting IP Address
Internet IP Address
Internet Subnet Mask
Default Gateway
DNS1
DNS2

Now Default Gateway is rather obvious, as is DNS = Nameserver, but which IP addresses does it want prior to that?
==================////////======
IP Address for eth0
Network MMask for eth0
Broadcast Address for eth0
Default Gateway
Nameserver................... DHCP for the linksys is pushing out an IP for anyone that will listen.
The knoppix OS is saying you have a NIC card and it can see it. if you do not have a NIC then you get no network adapter found. that is the mesg. You got 'Operation Failed'. What that says is the NIC card you have , did not get an Ip from the DHCP. this is good.

Lets give the NIC card an IP? when you run the NCC then next time instead of yes to auto get DHCP, click no "No" button.

then..... put these in.........
IP Address for eth0..................192.168.1.100
Network MMask for eth0.........255.255.255.0
Broadcast Address for eth0....192.168.1.254......mostlikely it will have this in there already, don't change it.
Default Gateway.......................192.168.1.1
Nameserver................................192.168. 1.1...................
These are the 1st IP address for the default DHCP range on a Linksys router.
Put these in to the questions. then and the bash prompt. ( click on the black, gray,white icon in the tool bar, next the orange house)
on my machine a black screen appears and has one line..........knoppix@{knoppix}$.................. ........
type "cd /" "return/enter/key"nothing else...........
type "sbin/ifconfig" ..........."return/enter/key" nothing else................
what do you see???????
you should see that eth0 has the information that you just put in...............