I had similar issue. Yestarday the HDMI output to my TV just stopped working. No driver was installed, no software changed, I have not touched any hardware, cables etc. TV worked fine, the video output from my HD 5670 worked fine on a TV, just the audio stopped working (the HDMI output device was present, but "not connected", as on the screenshot at the top of the thread).
Resetting the PC did not help.
Replugging the HDMI cable did not work.
But installing newest drivers DID help.
I think ATI has some serious bug in their HDMI driver code, it's been there for a long time and have not beedn fixed uet. I used HDMI on HD 3xxx on Windows XP few years ago and the problem sometimes occured even then. I hope they will find it and fix it someday, but for now it seems they are denying the issue exists