From what i understand your ATI HDMI is installed correctly but you don't get any sound output ob start up. When you re run ATI driver setup audio works fine. Is that correct ?
If that is so, there are mainly two possibilities.
1) Outdated onboard audio driver.
Reports from net indicates updating on board audio driver may solve issues with HDMI (Although seems unrelated)
2) Bug in ATI driver.
There is a known bug in new ATI driver which causes problem with HDMI. Downgrading driver to version 12.1 seems to solve this problem.
Source : http://www.avsforum.com/t/1409098/ati-6450-hdmi-audio-stops-working
Uninstall your current driver and install ATI catalyst version 12.1
Download link : http://www.techpowerup.com/159374/AMD-Releases-Catalyst-12.1-Drivers.html