It may be trying to reconcile the Xbox 360's IP address. I am not at my 360 now but if you can, choose to get an IP address automatically in the 360's network setup.
Take a look at this site, it is older but may have some good hints.
I keep thinking that if you connect from one ethernet card (360) to another (PC), that you need a crossover cable.
ChiefelfA crossover cable is $10-15 so I am thinking if you need one, why not get a network switch like I suggested above and avoid any lag -ICS can cause quite a bit of lag when gaming online.
Then you would have MODEM/ROUTER/GATEWAY-------> Network switch ------->PC
(and another cable directly to the Xbox)
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V
Xbox 360
I have not bought an ethernet switch which has 5 ethernet ports but i am not sure how to connect my modem to it as my modem connects to my pc through usb rather than ethernet.
p.s. it is a crossover cable that is connected from my xbox to pc.