I don't quite understand your question.
Is the graphics card going to the HDTV, or is the motherboard being connected to the HDTV?
For most computers you can only use one or the other, so you likely want to be using your HDMI output from the graphics card.
No SOUND:
1) Make sure the video card drivers are up to date and include HDMI audio
2) Use the video control panel, or right-click the lower-right audio icon (in System Tray) and change Playback Devices to be HDMI. For example, if the card was NVidia it might say "HDMI NVidia..."
Other:
Setting up an HDTV is also a little different from a normal monitor. It usually goes like this:
1) Video Control Panel-> HDTV section
2) 1080p_NTSC@60Hz (or similar as applicable)
3) correct overscan (I forget the wording)