@SkyesMagic Try clearing Origin's cache, and if that doesn't help, uninstalling and reinstalling Origin itself (the hard way). This wouldn't affect your installed games.
If these steps don't help, you may need to do the above again, manually uninstalling the problem pack before reinstalling Origin.
If that doesn't help either, please see EA_Mai's post here, specifically part 3 about contacting EA support. If you originally bought Ambitions from an unauthorized third-party seller, you may have received a bad code, and EA may have removed the pack from your account.
I just installed Sims 3 on a brand new more than adequate laptop and ran into this issue. Then I contacted EA support and they could only tell me that a patch would be released that would resolved the issue....with no ETA. Can someone from EA PLEASE tell us when this might be fixed? I have tried all of the before mentioned suggestions with zero results. I am beyond frustrated.
@Cellistina The EA support rep misinformed you—there is no TS3 patch coming, soon or ever, for any remaining issue. The game has been out of development for almost five years, with only a single patch since then. I'm sure the EA community managers would tell you the same thing, if and when one of them sees your post; I can forward it and try to get you an official response, if you'd like.
In the meantime, though, the usual steps are to clear Origin's cache, and if that doesn't work, uninstall and reinstall Origin itself. Since this is a brand-new laptop, though, it's unlikely that either of these would help. Still, you're welcome to try.
It sounds like the most likely explanation for this issue is that the packs have been blocked in your account. This could be a mistake, as has been known to happen. But if you originally bought the packs through an unauthorized third-party source, it's possible that you received bad codes. For a year and a half, EA has been systematically deactivating packs attached to codes that were originally stolen or otherwise fraudulently obtained, even though the players usually had no idea that there was anything wrong with their purchases.
To find out whether this has happened to you, and correct any mistakes, you'll have to contact EA customer support (again). If it was a mistake, it would be helpful for you to have any proof of purchase or ownership (receipts; photos of discs, cases, inserts; etc.) on hand for the chat. Rather than email, you may want to use a live chat or callback option so that the support rep can check your codes in real time and pass along the info.
So I just went and bought the stuff pack again. This time it did register on my origin account. Thanks for the help!