@rhiannnonn The fact that you were initially able to play the base game without issue is a good sign—it means you can probably skip the most difficult step to fixing the unknown error. But when you uninstalled TS3, the uninstaller probably missed some files, which is why you can't launch the game now. So the first thing to do is manually uninstall everything.
https://bluebellflora.com/how-to-do-a-clean-uninstall-and-reinstall-on-a-mac/
Then reinstall the base game only, and patch to 1.67 using the Super Patch (digital download version). Even if the game thinks it's already patched, it may not be, and the Super Patch can't hurt.
https://bluebellflora.com/sims-3-manual-super-patch-for-mac-1-67/
If the base game runs now, you can install HELS and LN. The reason that the game wouldn't launch after you installed the packs the first time around is that LN didn't have its own alias in your Applications folder, alongside the alias for the base game. But creating one is easy:
https://bluebellflora.com/sims-3-packs-not-showing-as-installed/
Please note that if you ever install any other packs, you'll need to use another workaround as well. (Luckily, there's a video guide for that, if you need it.) If you still can't get the game to launch, or you run into any other problems, please post your specs here, along with any error messages you're seeing.
gather mac specs: https://answers.ea.com/t5/The-Sims-Mac/READ-FIRST-Sims-3-Mac-Help-Guides-and-Troubleshooting/m-p/4756624#M4