Dave,
You are correct, you receiver doesn't process any audio over HDMI, it only does HDMI switching. You will need a digital optical or coax connection from each of the A/V sources to the Reciever. If you want, you can use the HDMI switching feature on the receiver or connect video directly to the TV.
So does that mean that I would have to run an audio cable from the receiver to the tv since the hdmi will not carry any sound out of the receiver? Would it be better for me to just leave the hdmi going from the cable box to the tv, then run an audio cable from the cable box to the receiver?