Ahem,
You are using modem and linksys switch?
No wonder, correct me if im wrong, but by saying switch,
I think this is what happen;

1.You connect both your computer and xbox to the same linksys switch.
2.Linksys switch work as a switch to allow only one connection at time.
3.So, if you are using internet on the PC, the switch disable connection for 360 and vice versa.

i using screamyx modem(billion) n dlink switch ... can using internet at the same time for both pc n xbox..

u need to set ur modem to auto connect ...