@Shad0wLoki is it possible you redeemed the product key within a different Origin account? The game shouldn't have disappeared, but it obviously wouldn't show up if you're not using the same account you did back then. Another possibility is that you received a bad code, and it was removed after the fact; this is always a risk when buying from an unauthorized third-party source.
If you can't figure out what happened to your game, you can always contact EA customer support and ask for help. A support rep would be able to tell you if the code was removed from your account or was still active but on a different account.
https://help.ea.com/en/contact-us/
EA Play is not required to run Sims 3, although Origin is if you buy the game directly from EA. Some of us instead buy and play through Steam; others still have original discs.
