Downloading SIM3

you need to get origin once you download origin http://www.origin.com/download  use the same email and password as you used on the sims 3 account as they will be tied to that account https://help.ea.com/article/how-do-i-download-my-new-game-on-origin  some times the game does not show up straight away log out and back in this gets the game to reload/refresh

also make sure to download the correct version of origin if your a pc or mac computer

http://answers.ea.com/t5/The-Sims-3/Information-How-to-Register-The-Sims-3/m-p/387162#U387162

if you still have issue with the invalid code message 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