|"The computer has a connection and pings"|
What does it ping? Other computers in your LAN or can you ping a website by IP or Domain Name?
On one of the working systems open a command prompt ( START>RUN>cmd )
type ipconfig /all and hit ENTER.
Note down the IP addresses for gateway and DNS servers
Now do the same in the problem machine.
Are the gateway & DNS details the same? Post back with the results.
Goin' Fishin' (Some day)