http://www.lg.com/ph/support-product/lg-BH6330H#

according to the manual that particular system only has an optical input and hdmi output (but it does support arc).

the only two ways which you can connect up to your computer are:

-optical cable from your motherboard or via a soundcard.

-if your tv has ARC support on hdmi then you could likely connect via hdmi from video card to tv and then from tv to home theater to pass through the audio via ARC support.
 
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