There are a number of possible problems.
First, make sure that your firewall is not preventing network connections. The best advice is to disable the firewall until you have a network set up, then enable it. Disconnect from the internet whilst doing this.
Secondly, to see other computers in My Network Places, you have to share a file, directory or drive.
Thirdly, make sure that both computers have the same workgroup name but different computer names.
On each computer, open a DOS window and type "ipconfig" [Enter]. The desktop will probably have an IP address of 192.168.0.1 on the ethernet connection and the laptop 192.168.0.2