Scowndrul is on the right track there, I would make sure your computer it trying to play the game in stereo and not 5.1. 5.1 has a lot of problems that we are currently working on fixing. Also, make sure that everything is set up properly in the in-game audio options. If you change anything, be sure to press 'OK,' simply escaping out of the menu won't save your changes.
To help us understand the problem, are champion voices still working correctly? And are the UI sounds like the menus and the shop still working correctly?