You seldom need to have your home wi-fi security key as your device usually remembers it and signs you in automatically. I help people with tech issues and recently I have had a few that needed to connect new computers or mobile devices to their wi-fi. However, they were unable to find their security key. Luckily, they had a PC that was connected, so I followed the directions in the article, “How to retrieve Wi-Fi passwords saved on your PC” http://www.pcworld.com/article/3018974/security/how-to-retrieve-wi-fi-passwords-saved-on-your-pc.html and was able to retrieve their wi-fi key.
I use a password manager and suggest to all to use and maintain a password manager of your choice. I use eWallet by Ilium Software http://www.iliumsoft.com/ewallet but there are several good programs available. Also see http://www.infoworld.com/article/3036606/security/review-8-password-managers-for-windows-mac-os-x-ios-and-android.html and http://www.pcworld.com/article/3085395/security/5-things-you-should-know-about-password-managers.html
Other ways to find your key may include checking the router provided by your cable company. Many times, the key is printed on the tag that contains the serial number. Also, check the installation papers from your ISP (Internet Service Provider) as the installer generally writes the key or it is printed on the work order. You may have to resort to contacting your provider’s tech support to change the key.