I do not have that HP but almost always it's a driver or setting issue. The good or bad news is that folk are solving it many times by checking the PC maker's web pages for drivers and the settings.
I have a HP Pavillion Elite m9040n PC connected to my TV via HDMI. The speakers are external. I have no sound from the PC, however my PS3 (also connected HDMI) does not have the same problem... The sound and pic are fine there.
I have updated drivers etc... The PC has never had sound, I have upgrades to 32bit Windows 7 and still nothing. I am a neophyte with this sound issue. Is there a simple newbie solution?