1. Try other HDMI cables. I won't say how many times that helped.
2. Besides the graphics driver, install the Intel chipset driver package.
3. Be sure the HP BIOS is current.
4. All that done or maybe before all this go get a current Linux distro on USB or DVD to boot and test with. I don't learn Linux. I use this in a no-install bootable USB stick to see if the hardware works in another major OS. I've used this advice for over a decade. http://tips.oncomputers.info/archives2004/0401/2004-Jan-11.htm

Be sure it's not in TABLET MODE. Noted at https://h30434.www3.hp.com/t5/Notebook-Video-Display-and-Touch/HDMI-video-and-audio-output-is-not-working-HP-ENVY-x360/td-p/6469798