No Audio, but the Drivers and Windows Audio Server are Running

If audio has stopped working, but the sound-card drivers and the Windows Audio Server are running, then I have bad news for you: there is no known solution. This page is here to save you from wasting many hours of your life. Take a deep breath, back-up all important files, and reinstall the system from scratch (or a backup if you have one). 

I encountered this problem after making the mistake of installing Windows XP service-pack 3 the day that it was released. After trawling the internet for solutions, trying various suggestions, uninstalling and reinstalling drivers, etc., I had wasted over a day. An old system backup that I had failed, so the final solution was a complete reinstall. This is the solution that most people eventually used. It appears that this problem existed as early as Windows 95, and that Microsoft still have not fixed whatever issue is causing the sound to disappear, and be un-fixable. 

In short, if the audio fails, do not bother trying to fix it; simply re-install Windows. If anyone has a better solution, please let me know.