@Anuaert I still think a badly-done account merge may be the issue here, but your dxdiag shows a couple of issues that should be addressed. First, please manually update the driver for your graphics card. You can get the newest copy directly from Nvidia:
Run the installer as an admin: right-click on the download and select "Run as administrator." Choose the custom install option and check the box to perform a clean install. Restart your computer when you're done.
Before trying to play Sims 3, please also do a clean uninstall and reinstall of Origin:
Next, download the full Origin installer and run it. Here's the direct download link:
Be sure to run both the installer and Origin itself as an admin: right-click on each and select "Run as Administrator."
If neither of these steps helps, I'd recommend trying EA Help on Twitter or Facebook. Ff the person you talk to doesn't understand the issue, please try again on Tuesday (or later) during U.S. business hours. And let me know there's still an issue; I'll ask around to see if there's anything else you need to say or do.