It really depends whether every port is assigned only a single IP. If the campus has a DNS pile big enough to run all the boxes, then a switch should do the trick (with the uplink port plugged into the wall). Both the PC and Xbox would get an IP from the DNS server. If you are only allowed one IP each, then the router it the best way to go.
Kolila is suggesting putting a second network card in your PC and using ICS to share the connection, but it is probably more hassle and not much more cost than a router anyway...
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who hid my keyboard's PANIC button?
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