On the Gigabyte site it lists that the latest Realtek audio driver
is version 126.96.36.19954, 104.11 MB and released on 2012/03/06 however on the second link you provided me, the latest one that shows up is version R2.68, Driver Version in Device Manager: 188.8.131.5202, March 30th, 2012 and 67762k...
I just went ahead and installed the one in the second link, linked to by Brink.
It asked me to restart so I did.
After restarting, I went back to the playback devices menu, right clicked on default Speakers and selected test and it still only plays from the right speaker. :\
Addendum: If I select configure speakers, it does give me more options this time (stereo, quadraphonic, 5.1 and 7.1) however mine are 2.1 and no matter which of those options I'd select, the sound coming from the left one still didn't work.