So I seemed to have found my own answer.
My Sony receiver supports HDMI pass-through only. So I can't plug my HDMI cord in and have it play audio through my A/V speakers. It passes through to my monitor speakers.
This forum post I found explains the entire thing: http://www.highdefforum.com/high-definition-lounge/37751-great-picture-but-no-sound-through-hdmi.html
It really sucks that in order to get full 5.1 audio I have to buy more cords and probably a sound card or an SPDIF hookup.