Just check a few details of the graphics card. Video cards do not have audio built into them, usually. However, HDMI output connectors certainly are supposed to have audio signals in them. And in the case of ATI cards (but not some others), they added audio signals to unused pins on DVI output connectors (DVI does not normally have audio) just so that you could buy the RIGHT KIND of adapter to "convert" DVI out to HDMI out (including audio). So IF you have such an adapter, is it the right kind, and is your video card one from ATI that has this feature? However, if your output port is a true HDMI in the first place, the adapter question in not relevant.
But one step that may be required in either case is, how do you get audio into the video card? In some cases there is a small cord you must connect from a mobo (or audio card) connector to an input on the video card to get it there. Does your video card need that?