Does it also help if you switch the display mode to windowed or fake fullscreen in the graphics options?
Do you get sound in the intro videos on startup, or when starting a new game?
Are you shutting down all non-essential programs before starting the game, especially anti-virus and anything sound related?
A couple of people have had sound problems caused by the Razer Synapse program running in the background, for example; one (with Razer Kraken headphones) had the sound cut out completely after a few minutes, while the other (with a Razer keyboard and mouse) was getting sound stuttering.
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?
If you right click on the volume control in the task bar and select Playback devices, you can test the available audio outputs, and switch which is default. The game itself doesn't have an option to switch outputs, and just uses the default.
One person that lost the sound in-game just said that they made changes to the default playback device to fix the problem. Another using headphones unplugged them, switched the default to speakers, plugged them back in and switched it back to the headphones.
Since there is something different between the game being full screen and minimized, changing the default playback device, and possibly back again, may reset whatever the issue/setting is.
Try exiting out of the Steam client completely, and starting the game directly from the '..\SteamApps\common\Divinity Original Sin\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 8 compatibility mode.
Try verifying local files: in the Steam library, right click on Divinity Original Sin Enhanced Edition and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Cache...' button.
