Is it possible that you're using a different like, login for your connection?
For example, we're on AOL and there are parental controls. When I was like, 12 and 13 years old, my Mum would make her boyfreind set it so I couldn't look at 'any inapropriate sites'. This not only blocked teh sexi pr0nz, but also blocked my access to MSN, Xfire, AIM, 99% of online games, various IRC chat rooms, and almost everything internetlike.
If you're connecting to the same router, with the same connection on your desktop as you are on your laptop, I really don't see why it shouldn't work.
Check your host file on your Desktop. It can be located at C:\WINDOWS\system32\drivers\etc
There are two, make sure you can see the 'hidden' files. It should be the 'hidden' one, it's an "MSN File" iirc.
(Tools > Folder Options > View Tab > Show Hidden Files and Folders)
Open it with Notepad. Inside it should only contain one line, which is
127.0.0.1(Tabspace)localhost