Shawn,
Okay. Let's see if we can get you all set up. It's true that some receivers cannot process the audio from HDMI, but your receiver can. That said, there are definitely ways to send the audio on a separate line and have your receiver use it. I'm going to be referencing your owner's manual for the 3806, so in case you don't have it handy, you can download it from Denon at the link
here.
I'll poke at one other possibility, because I didn't ask it last time. Are you getting no sound over HDMI on the Denon, or on the TV? I want to ask because you can't have both. In the receiver's menus, you select if you want the Denon to process the audio from HDMI or to pass it on to the TV. It can't do both of those. Setting this up is described on page 66 of the manual, specifically under item "4" of the "Video Setup" section. This might be your issue.
If that doesn't help you out, then you can connect another digital audio line from the DirecTV receiver to the 3806. You can use either an optical or digital coax connection, whichever your DirecTV receiver has. If it has both, then use either one. Once done, you need to assign that input (in other words, tell the Denon which jack on the back of the unit you used for the DirecTV input). This is covered on page 63 of your owner's manual.
These are just a few things to get the ball rolling. Please let us know if this has solved your problem, or if you still need additional help in getting it all set up the way that you want.
Adam