Cognition Episode 4’s saved games stored

32 bit games can run 64 bit Windows, typically without any issues. Older 16 bit games designed for Windows XP or earlier will not run on Windows Vista/7 64 bit.

Many times, software and games will claim they do not run on a particular operating system (Windows Vista 64 bit in this case) simply because they don't want to allocate resources to test on that particular system or support it. According to this forum post, Medal of Honor: Airborne runs just fine on Vista 64 bit.

First of all I suggest you to check the source that you used to install the game. Is it a retail box copy? Does it come from digital services like Origin or Steam?

In case of digital delivery try use game cache verification (Steam has this function, I don't know the other services) and then try to uninstall the game and reinstall it, in any case.

If the problem is not solved could be that you miss an important system update. It seems that the DLL D3DCOMPILER_43.dll has been released in June 2010 DirectX SDK. You can try to install this DirectX 11 Technology Update and see if it fixes the problem.