I ran across this same issue recently with my Dell Latitude running an Nvidia NVS3100 mobile graphics card, using a similar adapter to a 24" HDMI Dell monitor and from researching, I found that Audio is an optional signal with Displayport 1.1a. Most hardware these days is enabled, but updated drivers are a must, which is why the support told you that. Quite rude to shut you down without giving you a link to the driver, however.
The HP forum thread below may have a solution for you, as they're using similar setups and have found working solutions. I don't have an actual solution here, I'm merely trying to be of use as I struggled to get my issue resolved recently and I know what a pain in the butt it can be!
I also just found these tips that might work for you:
On a machine with a discrete graphic card - just choose NVidia HD audio as playback device after connecting your display.
On a machine with an integrated graphic card - the trick is to go to Control Panel > Sound control panel > Right click on your TV > Select 'Set as Default Device'. Then you should start hearing audio out from the TV speakers, and the green sound volume meter beside the TV in the Sound Control Panel should start responding to the audio you're playing.