Connecting our laptop

In order to retrieve the wireless network key you have to log on to the web interface of your router. Depending on the router it can be anything from 192.168.0.1, 192.168.1.1, or 192.168.1.254.

Your can find this IP address in another way, but you need a computer that is connected to the router via an Ethernet cable (in case wireless administration is disabled.)
Once a connection is established, open a command prompt (Go to start -> Run), type "cmd" and hit "Enter".
In the following command window type "ipconfig" and hit "Enter" again. The value after "Default Gateway" is the IP address of your router.
Type that into your browser. Don't type www.etc., simply (in my case) "http://192.168.1.1".

This leads you to the web interface and depending on your router, you will find your wireless settings somewhere. From there you can access and reset your wireless network key or copy it.

If you have any more questions or get stuck at one point, just come back here and leave a comment (with more details about your router) - I'm happy to help.