I've wrestled with this issue for some time trying to help a squadmate, and read this thread, together with many others, trying to find a solution. My Cougar works fine, and always has, in Windows 7. My squadmate, no matter what he tried, could not get away from the "The program can't start because sttubedevice203.dll is missing" message.
It was particularly frustrating because it didn't seem as if the file WAS missing; it was there to be found in the "drivers' folder.
Where it wasn't was in <System Drive>\Windows\SysWOW64. It should have been.
Once the file was copied from the drivers folder to SysWOW64, the message went away and the HOTAS files worked fine.
I hope this solution works for others, too.