@mmarch What are you looking for? The base game and expansion packs have five groups of 4 characters for the activation code. Worlds have four groups of 4 characters for the activation code. Prior to Origin the code was stored on the local computer and it was up to the user to keep track of the code. The codes were stored (and still are) in the registry of pc computers. Some very early codes will not work anymore and there were some instances when the codes supplied by some authorized vendors were incorrect. It is important to know when and where you purchased the game. If you want to contact EA customer service - link - EA customer service If you get the call back option this does work. If you use the chat it works best with IE (Internet Explorer).
@CoWgirL_4u Right-click on the Sims 3 icon and select Game Properties, not Game Details.
If you can't find your code, you can always contact EA customer support to ask for it. A support rep should be able to read it to you over the phone, or paste it into a live chat window.
If you have other questions, it would be best to start your own thread; this one is pretty old, and Origin has changed a lot in the interim.