Please see http://www.officeforlawyers.com/howask.htm
Specifically we need to know more about what's different between the two computers. How are they connecting to the router? (Wired? Wireless?) What kind of router is it? What kind of firewall are you using?
Can you ping the router from the computer that doesn't connect to the Internet?
Do you have SP3 for Windows XP installed?
-B-