What?

Your running both systems on the same MAC address???
Are you crazy??? That's just going to lead to network errors and cause internet connection problems... MAC addresses are similar to IP addresses... If you have 2 people with the same IP on a network then you'll get a conflict... and it won't work..
You will need to either change the MAC address of you computer or the one of your xbox to get everything working...
From Windows XP this can be done by going to the control panel and selecting network connections. Doubleclicking on your NIC and selecting properties.. From there select configure.. Then go the the advanced tab and select network address from the combolist.. Now just fill in your new mac address and hit ok...
You might need to restart your computer.. That should solve your web-surfing problems.