That's because the Radeon card incorporates an audio chip, and since you've installed the entire driver package (which includes the card's audio drivers), the motherboard's SoundMax audio chip has been disabled to avoid a resource conflict.
What I did is this:
1) I uninstalled the entire Catalyst Suite for the Radeon card
2) Run the Catalyst installer again but choose "Custom" install.
3) In the custom install menu, deselect (untick) the "audio drivers" then continue with installation.
4) After a Windows restart, your motherboard's audio should work okay (you may need to install SoundMax driver one last time but it shouldn't be necessary).