In Documents, you have a folder called The Sims 3. Move it or rename it. Start your game (don't forget to download and install the last patch). A new The Sims 3 folder will automatically be generated. Quit the game. In the new The Sims 3 folder, create a new Mods folder, create a new Packages folder in the mods folder, copy and paste the resource.cfg and packages where they should be (don't copy and paste the whole folders from the old The Sims 3 folder, it's safer to copy and paste the files individually because sometimes folders and their content can have issues, sometimes due to invisible files in them). Delete the 5 cache files (as explained above). Restart the game and see if mods work.
If mods still don't work, get the Sims 3 key to download it from Origin. Open iTunes, open the Store tab, log into your account. In the menu bar, click "account --> View my account...". Your account overview should have a purchase history with the date of the last thing you bought. Click "show" in order to access detailed purchase history including all your orders. Click on the Sims 3 order to view details. Normally, you should have access to the key at this point, on the detailed order. If there is no key, contact Apple Support because it's your right to access the key as you bought the game.
