how do you have the xbox wired to the modem? do you have the modem running into a switch/hub so your computer and xbox can both share the connection?

you shouldn't even need to put in the dns servers, most modems and routers will automatically enter that stuff in thru DHCP by default. if you have the wires all connected correctly and dhcp works.. it's almost a matter of just turning the xbox on..

one way you can get the dns servers tho is to go into the network config for your computer and the dns servers will be listed in there, it'll be the same dns for every system you run.