16 digit codes are usually for downloadable content game codes are 20 digits long and you use the registier a game this way
Click on the My Page tab.
Then click the My Account tab.
Click on Register a Game.
Enter the product code for the expansion pack or stuff pack.
Click the green Register button.
see if this FAQ can help http://answers.ea.com/t5/The-Sims-3/Information-How-to-Register-The-Sims-3/m-p/387162#U387162
if you continue to have issues or you end up getting an invalid code or used code then contact CS
They can be found here: https://help.ea.com/contact-us
Choose a category, a game and a platform for the contact options to show up.
If live chat is gray, change your country to US and make sure you're on US Business hours. It might also gray because they're very busy. Try later.
See this post if you have trouble with the site: http://sims3.crinrict.com/en/2012/10/how-to-contact-ea.html
