I'm having the same problem! Or at least similar. Though a lot of my other Sims 3 games that I had already installed before on a different computer were already on my origin account. I never registered my Sims 3 Supernatural game, now it's telling me that myproduct code is invalid. Could this really have been because someone else entered the same one? This is the same thing that is happening with the Sims 3 Into the Future game that I JUST got for Christmas. Like today. I got the disc from my mom, and instead of inserting the disc, I just registered the game and tried installing it off of my Origin account.
Maybe I should go back to the beginning. I reinstalled all of the Sims expansions on my new computer, and every one of them was fine. Then like, three of them (including the one I just got for Christmas), when I clicked "Download" from origin, it said something like "It's already installed on your computer, go uninstall it from your computer and then re-download it from origin," though it isn't even on my computer at all to uninstall in the first place. When I inserted the Sims 3 Supernatural disc when first installing it on the new computer, it just would not come up! Which is why I tried the other route of registering it and downloading it from Origin.
I am feeling very frustrated! Do I really need to go buy all these games online again so that I can get a game code? If so, then that is just plain ridiculous. I can prove that I have the original game and the code inside it, and also from my purchase history too!