HDMI does pass audio from you PC. What you need to determine is whether or not your receiver does audio pass-through or not via HDMI. What audio pass-through means is your receiver would not utilize the audio signal coming in through HDMI and just passes it through the HDMI out to your HDTV. My Onkyo HT-R370 does this, so I connected audio from my PC to my receiver using the digital optical port on my sound card. Now you do not necessarily need a sound card as your PC is brand new. It likely has on-board digital audio connections that will work just as well.
First thing to check is whether your receiver accepts HDMI audio or if it passes it through. If it accepts HDMI audio, this is the way to go. If not, use the on-board digital audio out from your PC (assuming it has it).
mmm...but then my audio woudl have to go through my video card on my computer right? Does it do that? I know I tried to just hook up HDMI from PC to Receiver and I didn't have any sound. I assumed I had to use the motherboards on board sound (no sound card)
Any of the HD series ATI cards (HD2xxx through HD5xxx) can do audio through the video card. Not sure about NVidia cards. Check to make sure your graphics card is the primary audio device. I seem to recall reading that newer drivers for ATI cards have some how messed up the audio signal and that you shouldn't use any drivers newer than the 9.8s, but I can't find the thread now.
If you can't get it to work, there's nothing wrong with using your motherboards on-board coax or optical S/PDIF (if it has it).