Installation of the HD 4350 automatically updated your default audio playback device to the HDMI slot on the graphics card (it doesn't matter that you're not using it). Go into Control Panel --> Hardware and Sound --> Sound. This should bring up a list of installed audio devices; one being ATI HDMI Audio and the other being either a sound card or on-board audio (based on what else you have installed in your system). Change the device to the on-board audio (may be listed as Realtek or other on-board audio source). Click Apply and then OK.
If you are unable to do this, you may need to update Windows Vista. If you are able to do this and it doesn't work, try re-installing the drivers for the on-board audio (sound card if you have one...