The graphics (video) driver controls HDMI audio. Most likely installing Win10 resulted in the loss of the driver that worked for you before.
Your model has Intel integrated graphics, plus either nVidia or AMD discrete graphics. You can find all of the graphics drivers that Dell released for the M17x on the Alienware M17x html page. Scroll down to the Video section. Of course there are none for Win10, so you might have to use Windows compatibility mode to install the drivers meant for a different OS.
You might also try opening the Recording tab of the Sound properties (right click the audio icon>Recording devices), then right click in the list of devices and put a check mark in the option to show disconnected and disabled devices. If HDMI audio appears in the list of recording devices, enable it and make it the default device.
Finally, you might be able to get some additional advice from the Alienware Club discussion board -- they know a lot more about Alienwares there.