That helps a bit. Found three variations of it here,
Search HP US - Search results for 'dc7700pc'
different forms/cases, but all three have Realtek HD for audio (based on the available downloads. First thing to do is double check in the bios that the onboard audio is enabled. I'm assuming you have an AMD or Nvidia card with native audio on it for HDMI use, if so yours wouldn't be the first HP I have seen where when one of those video cards is installed the HP bios also sees it as a sound card being installed and it will auto-disable the onboard audio.
If it is disabled in the bios, grab this,
Latest Realtek HD Audio Driver Version
for the
driver for it, as the one from HP is somewhat (more like quite a bit) older than the latest available from Realtek.