I'm trying to register my game on Orgin but it keeps saying my code is invalid

See instructions here: http://answers.ea.com/t5/The-Sims-3/Information-How-to-Register-The-Sims-3/td-p/387162/

If that doesn't help, get in touch with a customer support game advisor

Game advisors can be found through live chat.

1. https://help.ea.com/en/contact-us/ 
2. Click on the orange NEXT button
3. Select a platform
4. Click on the orange NEXT button
5. Select a topic and describe your problem in a few words
6. Click on the orange NEXT button
7. Click Chat Now to chat with a Game Advisor
   

In Details here: How to contact a Game Advisor using the new EA Help page