If you start a new game do you get audio in the intro video?
In the audio options, do you get a sample sound played if you move the FX, Ambient and Voice sliders? The volume of the music should change, as well, when you change its slider.
Did you try changing the sound quality in the options? You could also try changing the Windows sound quality settings.
If you are using speakers, do you have headphones you can try, or vise versa?
Are you shutting down all non-essential programs (especially anti-virus) before starting the game?
One person using Razer Kraken headphones reported the sound cutting out after playing a couple minutes, due to having the Razer Synapse program running in the background.
If you open the game, then either Alt-Tab or switch to windowed mode, click on the Windows volume indicator and open the mixer, is 'DOS EE' listed with the same volume level as the main slider, and not muted? It probably isn't muted, but something is treating the sound through at least the startup video differently than directly from the game.
Did you check for updated sound drivers?
Try exiting out of the Steam client completely (if applicable), and starting the game directly from the '..\SteamApps\common\Divinity Original Sin Enhanced Edition\Shipping\EoCApp.exe' program file, by right clicking and running as administrator.
If that doesn't help, try right clicking on EoCApp.exe, select Properties, switch to the compatibility tab and try a Win 7 or (if available) 8 compatibility mode.
