Old Sims 3 expansion packs

@bella_guz33  If the old computer worked at all, even a little bit, you might be able to find the product codes in its registry:

https://sims3.crinrict.com/en/2013/09/how-to-find-your-serial-number.html

The only other suggestion I have is to contact EA customer support and ask for help figuring out what account registered these codes.  A support rep wouldn't be able to tell you outright, but they might be able to give some hints.  If you can then establish that you're the owner of the account, you could request that it be merged with your current one.

I strongly suggest using live chat rather than email.  If you're not seeing the option, try this link:

https://help.ea.com/en/help-contact-us/?product=the-sims-3&platform=&topic=missing-game&category=manage-my-account&subCategory=find-missing-game

Make sure you're signed into an EA site (this one is fine) before clicking the link and that the location in the lower-right corner of the browser window is set to U.S. or U.K.

Other than that, there's unfortunately nothing you can do to recover the codes.  But you could install via disc in Windows at least, provided your base game disc was manufactured prior to September 2012.  (The newer ones require Origin, now the EA App, to be present and managing the install process.)  That's not ideal if you'd rather play on your Mac, but it might be better than nothing.  And the 64-bit Mac version has its own problems even beyond the usual Sims 3 issues, so it's hardly ideal either.