You are getting that error message because each code can only be registered once, and once registered in one account, you don't need to use your code to install the game anymore, just your account.
Do you remember having registered your games in Origin or thesims3.com before? Does The Sims 3 game show in your Game Library?
Download the Origin client here: http://origin.com/downloadLogin and you should find the game in MyGames to download.If it's not already there, there should be an option to register the game somewhere.
Check out our Sims forums for tutorials and all things Sims.
Try these steps first to clear up any problems you may have when connecting to an EA game.
We'll make sure it's you by sending you a code for your trusted devices.