The OP states it works on his laptop and not his desktop so I'd say his router is fine.
As someone has already mentioned but you never replied, ping the website address from a command prompt from both machines and check that the IP address that comes back is the same. That's a start at least. If the IP addresses are different and you have flushed DNS, check your windows host file to see if an entry exists in there.
If the IP addresses are the same then try a traceroute and see if both machines are taking the same route. Again mentioned above but you didn't respond.
If they are both taking the same route, try a linux live CD like ubuntu and try the internet from your desktop and see if it works. That will rule out a physical route issue for whatever reason.