You are probably looking for a network key from your router. I assume this is to allow another computer to access your router so that you can both be on the network. On the working computer, you need to go to the website that accesses the router.
Go to START menu
Go to Control Panel
Go to Network Connections
Go to Network Connection
Double Click on Wireless Network Connection
Click on Support Tab
Look at the Default Gateway. It is probably going to be something like 192.168.0.1 depending on the brand. That is what my D-Link is. If you can't find one, 220.127.116.11 or search the Internet for your brand.
Enter that number into your browser and it should access the router. From there, you need to look around for what you need. It varies with manufacturer, but some have help or a wizard you can use.