August 2017
August 2017 - last edited August 2017
The games generally do not simply disappear. It might be possible that you very simply are getting confused with the Origin's layout.
Here is a guide which helps in trying to find missing games in your catalogue : https://help.ea.com/en-us/help/origin/origin/origin-my-games-list-is-blank/
If all else fails, you can contact the support directly from here and they should be able to help you out : https://help.ea.com/en/contact-us/
The code themselves are usable only a single time so it would make sense that they're already in use as you have used them up once in the past. And since they bind to a single account, they should be there where they got first activated once we first simply find where they are.
Good luck.
August 2017
If you have the CD games try reinstalling them... Origin will come up and your game will show up... or at least your original (Base game)
your EP will not show up but they should be in the Sims 3 launcher...
Hope this helps,,,