As usual, make sure you backup your The Sims 3 folder before making any of the changes below. A number of files will be deleted in the process, and if something should go wrong you can re-copy your Sims 3 folder from the backup.
In your The Sims 3 folder, go into DCBackup and delete all of the files in there (including ccmerged.package if it's there).
Delete any .ebc files in DCCache.
Delete the contents of the Library folder. *
Delete the contents of the InstalledWorlds folder. *
In you main The Sims 3 folder, delete the following files:
* Note, if you're doing this from a Factory Reset or a fresh install, you will not have anything in your Library or Installed Worlds folder.
Now, re-install your Store content. Once that's finished, close and re-open the Launcher. If all went well, you should see most or all of your items on the Installed Content tab of the Launcher. Otherwise, follow the steps again.
If successful, it is highly recommended to create a backup copy of this The Sims 3 folder in a safe location.
I really hope this helps people having this problem.