@addalily You described it fine, and it's a common issue. Please start with a clean user folder: move your entire Sims 3 folder out of Documents > Electronic Arts and onto your desktop, and a new folder will spawn the next time you open the launcher. Don't add anything yet; just see whether you can start a new save.
If the new save works, you can start rebuilding your content. Most of the files—saves, mods, saved builds, etc.—can be transferred, but it sounds like it would be best to reinstall your store content from scratch. So try that first, and keep testing the game to make sure you don't get another black screen. It's best to install only a few items at a time; the launcher doesn't handle large amounts of data very well. Worlds should be handled separately, not in a batch with anything else.
If you're installing content from the Exchange, not just EA-made store items but player-uploaded content as well, be sure to check the launcher's Installed Content tab after installing anything. It's possible for bad custom content to be attached to Exchange downloads, and if you get some, you'll want to uninstall it immediately. If installing a particular item causes another black screen, you may need to just avoid it entirely.
Once your store stuff is installed properly, you can transfer the rest of your content to the new Sims 3 folder. It's a good idea to do so in batches though, testing each time, in case there's another corrupt file somewhere. Here's a list of the files in your user folder, so you'll know what to transfer and what you can leave behind:
https://sims3.crinrict.com/en/2011/01/faq-user-files.html
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I don't work for EA. I'm just trying to help fellow players with their games.
