Sound mostly not working in Skyrim

Your problem is most likely related to your sound card drivers. After some searching the web i found that downloading the DirectX End-User Runtime Web Installer the problem was fixed. You can download the software HERE of the official microsoft website. This problem has been reported after upgrading your game in OS. (from vista to win7 and from win 7 to win 8). This solution fixed most problems. Hope it helps.

Okay, so this is quite a weird one, but could be helpful to others!

Basically, the headphones I'm using (Turtle Beach PX22) seems to have some kind of "minimum input volume" requirement, otherwise it gets filtered out as background noise. The solution was to set my computer's volume to 100%, and use the in-line amp to adjust volume instead. Now the headphones receive the full audio input and handle it correctly.