Would I be right in guessing that this connection is an ethernet cable going to your PC? And the same cable is also used to connect up the 360?
If you've got two ethernet ports on your computer then you can bridge the connection and connect the 360 to the net via an ethernet cable between the 360 and the PC.
I've got it working with my PS3. And it shouldn't be that much different to get it to work with a 360.
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