I deleted my DC Cache folder as well and my tabcasts stopped working. Which was why I bought the whole set so I was annoyed
But I really didn't want to uninstall and reinstall my game either, and I didn't want to lose my game since I had been working on it for over a month and I had my couple ready to have a baby finally. So I wondered if doing a factory reset, like in this thread
http://www.carls-sims-3-guide.com/forum/index.php/topic,7507.0.html would work.
Following the directions I renamed my Sims 3 folder in my documents and started the game.
Then I created a person and quit, saving the file.
I went onto the Store and redownloaded just the Oh my goth set (or whatever it is called) and installed it into my new game.
I loaded my new Sim and had her buy the MultiTab and listen to a tabcast to see if it would work. (It was funny because I randomized her when I created her and she was a technophobe so her whole mood went to Yellow just because she was listening to the tabcast!) and I waited until the tabcast was over and she did learn the skill.
So I quit the game and opened the Downloads folder in my new folder to see what the package files name was.
I then copied everything BUT what was in my new Downloads folder from my old one and pasted it in the new Downloads folder. If you didn't care about your old saves at this point you would be done.
I reloaded my new game to make sure the tabcasts still worked, and they did. So far so good.
Then I renamed the New Sims 3 folder to Sims 3.2 and renamed my old Sims 3 folder back to Sims 3.
(I probably could have done this step before I started, but I didn't know if any of it would work) and loaded all the games I wanted to save and deleted all MultiTabs from all my sims inventory. Then I saved the game and moved on to the next until I was done.
I then renamed Sims 3.2 back to Sims 3 and the old Sims 3 back to Sims 3.1. I copied the save files I wanted and pasted them into the new Sims 3 Save folder.
I loaded one of the games, bought a new MultiTab and listened to a TabCast. It worked!!!
So if anyone broke the TabCast by deleting the entire contents of the DC Cache folder this did work for me. It took about 45 minutes to do, so it's not a quick fix, but a lot quicker than uninstalling the whole game and reinstalling it! Thanks to MoonsAreBlue for the idea of the Factory Reset.
I hope this is clear