your video card likely supports sound out via dvi.
in this case a dvi-to-hdmi cable should work fine for both audio and video.
i have this exact setup with a gtx470 which is an older card. i've heard of issues with cheap hdmi-dvi cables but quality cables should be fine.
disconnect the auxilliary audio cables as you should not need them unless of course your video card doesnt support sound out which i do not see why it would not.