Please install the June 2010 DirectX runtime package, then use the DirectX web installer, as your current DirectX may have become corrupt over time.
You can find the ZIP file containing the 2010 package installation files here.
You will have to extract the files into some folder, then open that folder and launch the DXSETUP.exe file in order to proceed with the installation.
Afterwards, download the latest DirectX web installer and install it as well.
We will also introduce the necessary DirectX installer into the game's installer soon.