Sims 3 Launcher Not Working

@alexmaxzac  The chkdsk results look fine overall, although you'll want to keep an eye on the overall health of your hard drive.  The few bad sectors found aren't an issue all by themselves, but if they keep accumulating, it's time to get a new hard drive.  If you'd like more info on how to monitor this kind of thing, let me know.

The Sims 3 errors in your dxdiag reference .NET Framework 4.x, but the game uses 3.5, and so should the launcher.  Regardless of why that's happening, it's easy enough to address both issues.  First, run a couple of basic checks on your Windows system files; sfc should repair any .NET 4.x issues.

• Hit Windows key-X
• Choose either “PowerShell (Administrator)” or “Command prompt (Administrator),” whichever option is offered
• Inside the window that appears, copy and paste “DISM.exe /Online /Cleanup-image /Restorehealth” without quotes into the window, and enter
• The system will start validating soon. If it throws an error, please list it here
• After it reaches 100%, hit Windows key-X again
• Again, choose “PowerShell (Administrator)” or “Command prompt (Administrator)”
• Inside the window, copy and paste “sfc /scannow” without quotes into the window, and enter
• Post the message you receive here

Restart your computer, hit Windows key-R, and enter "appwiz.cpl" without quotes.  In the File Explorer window that opens, click "Turn Windows features on or off," and you'll see something like this:

.NET 3.5 is at the top, in blue.  If the box next to it is filled in, that means it's installed; click it to uninstall.  When the process finishes, restart your computer and repeat the above, except this time, click the box to reinstall.  Restart again before trying to play.