Re: activation code
16 digit codes are usually for dlc content to find your game code try this log into your origin account right click the game icon-show game details your code should be there if your still logged into origin log out close origin restart origin log back in to refresh/reload the game then right click the game icon-show game details make a note of your code have pen and paper handy (also be sure to use the same email and password for origin for your the sims 3 account as this ties the accounts together) if you used two different ones again contact CS
once your game is regestired in origin you do not need to regestier again on your sims 3 account
http://answers.ea.com/t5/The-Sims-3/Information-How-to-Register-The-Sims-3/m-p/387162#U387162
if you get an invalid or already used code then you will need to 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