CordeliaDoll Please check your antivirus for recent actions involving Sims 4 or the EA App. If you see anything, whitelist the program, or set exceptions for TS4_x64 and TS4_Launcher_x64, plus TS4_DX9_x64 if you ever use DirectX 9 mode. Set an exception for EADesktop.exe too.
You can also launch the game with the EA App in offline mode. If you can at least get to the Main Menu, disable SDX updates entirely, then quit, restart your computer, open the EA App in online mode, and see whether the game works.
If you still can't play, please let me know what happens now when you try. I see the screenshots, but all of those are from a game that has at least loaded to the Main Menu.