Re: How to view the registration code of a game already registered?
You can download the Origin client and download your game from the "My Games" tab. Remember your Origin and Sims acct need to be linked (i.e., you should be using the same email and password for both). If you do not want to do that, you can contact EA for the code, but the wait times might be long. Here is a link to contact them: https://help.ea.com/contact-us
Also, here's a post on how to navigate the contact page in case it's confusing: http://sims3.crinrict.com/en/2012/10/how-to-contact-ea.html (Just so you know there is no longer an email option, only live chat and phone.)
Best of luck.