1. The latest DirectX is 11 but for the game DirectX 9 is needed. Please make sure that it is properly installed by downloading the installer from here: http://www.microsoft.com/en-us/download/details.aspx?id=34429 and seeing if it determines it is installed properly. It will offer you installation of Bing toolbar so make sure to uncheck the field if you do not want the toolbar to be installed.
2. Reinstall your GPU drivers. To do so completely follow these steps:
Uninstall all of the Microsoft Visual C++ redistributables that you have installed.
Once it's done install the Microsoft Visual C++ redistributable packages from the link below starting from the oldest ones (skip the "arm" files). Launch all the executables as Administrator.
3. Disable all unneccessary apps before launching the game (especially apps with overlay) such as:
4. Please try launching The Witcher in a clean boot mode. Here is how to perform clean boot - https://support.microsoft.com/en-us/kb/929135/
If none of the above will help, please report the issue to us, if there is any information or error code displayed please make sure to include it in the description.