@beefpetunia Did you check the power connectors as described? If not, please do so now.
If that's not the issue, I'd like to see the results of some hardware monitoring. Please download hwinfo (it's free) from here:
https://www.hwinfo.com/download/
You don't need to install anything; just choose the Portable version, unzip it, and launch it from Downloads or wherever you like. If you do want the full installer, be sure to click the button for hwinfo itself, not for lansweeper.
Restart your computer, open hwinfo, choose Sensors Only, and click the button that's a sheet of paper with a + to start logging. Save the log file to your desktop for easy access. Wait five minutes, then open Sims 4 and play until it or your computer crashes. The log should be intact up to that point even after you restart. Don't alt-tab out of the game or run any other programs, aside from the EA App of course, while you're testing.
Please upload the log to the third-party filesharing site of your choice (Google Drive, Dropbox, etc.) and link it for me. Either leave it in .csv format or, if you're going to use OneDrive, create a .zip file, and don't open the log before uploading it, or else my log reader might not be able to interpret it.