@PinkLizzy14 Store content and custom content are installed into two separate types of files in DCCache: the store stuff ends up in .ebc files and the cc is in .dbc files. Store content is also encrypted where cc is not. So it's easy for someone's store items to stop working while their cc is intact.
Anyway, since your store stuff won't install, please remove all associated files from your Sims 3 folder in Documents > Electronic Arts. Go into DCCache and remove all the files except for those that end in .dbc (i.e. leave the custom content intact but remove everything else). Go into Downloads and remove all the store downloads you recognize, or just move the entire folder elsewhere if you don't need to save your custom content downloads. Removing these files won't uninstall anything; the files are extraneous once the content they contain has been installed. Finally, go into InstalledWorlds and delete all the store worlds.
Now try downloading one small store item and see whether you can install it. If that works, check in-game to make sure it shows up. If it does, install a store world that isn't Aurora Skies and check again. If that works too, you can install the rest of your store content in small batches, no more than about six items at a time—the launcher doesn't handle large amounts of data very well. Worlds should be handled separately, not in a batch with anything else.
If you get an error, or the store content stops working in-game, at any point, stop there and let me know. Please post the error as well, either a screenshot or the full text written out.