Most modern computers do not care about crossover cable and figure out the connection in hardware. What you're probably missing is the IP configuration on both ends.
To check that you can actually communicate, set following IP addresses:
On your laptop: 192.168.10.10, Netmask 255.255.255.0
On your desktop: 192.168.10.11, Netmask 255.255.255.0
Do not fill gateway/DNS addresses, restart if asked to.
Open command prompt on both computers, execute "ipconfig", and make sure you have IP addreses. Then try
on your laptop - you should see four lines with timings. This will ensure that you can talk to each other. If that's OK, you can use ICS (Internet Connection Sharing) on your laptop' WiFi card to share the internet with the desktop.