Which video card does it have, and do you have the latest driver
for it installed? Dell has downloads for all three of; AMD , Nvidia and Intel, most of which can't be considered recent. The audio driver for the HDMI on the video is included with the video card driver. With it being a desktop you should be able to get the appropriate driver directly from the manufacturer instead of what Dell has to offer.
Also when in the Windows audio properties make sure to right click and put a check nest to both disabled and disconnected devices, if you haven't already.
P.S. mrdemon you don't have the driver for your onboard sound installed, it is using the generic default Windows driver.