Hmm.. Came across a few problems people with MSI 970A-G46 were having with Linux.. but nothing directly sound related. (I have never used MSI, I always get Asus.. so I am flying blind)
They either had problems with USB, or some VMWare problem (I don't think that has anything to do with your sound ;)), and a couple of folks that had issues with their HDDs... they had failed to run as AHCI.
There seemed to be an issue with BIOS, one user has to downgrade his to get USB to work.. hmm, Have you flashed to the newest BIOS? If you have, maybe try downgrading like he did.
There was a mentioned MSI Linux (quick-boot) you can install called Winki 2... but is doesn't seem to be a full OS, just mainly for Internet connection o.O ...
Anyway, these 2 links show a little info about your MoBo (from benchmarking site) that the MSI site didn't show (and all "known" friendly Linux Distros, which you mentioned trying Ubuntu and Mint.. there are a few more there.):
MSI 970A-G46 Components
ATI SBx00 Azalia (Intel HDA) (Supposed on-board sound)
I noticed that it has UEFI; not sure that would give a problem with sound, but I know that it is dreaded in the Linux world :p I myself haven't had to worry about that yet.
I suggest seeing if Win8 (if you have it) works.. if it does, then (supposedly) Linux should work.
If it doesn't, or you don't have it, try another couple of Distros. If those fail, maybe take the MoBo for replacement.
(Although I don't prefer MSI, the stats on that MoBo look really nice; I hope you can get it to work!)
Yes faster is always better....Cutting and pasting stuf ///like FreeRepublic is much , much smoother on my AMD 8120 than on my AMD A6 APU Llano.
Both have 8 Gbyte memory and similar HDD's.
The A6 bogs down if a get a few windows open,...The 8120 can allow me to have a lot more stuff going.
I have about 80 tabs visible on FF, and 9 documents open, plus Thunderbird and a couple Bible programs and other things running, and things work well until i get down to about 1300mb of free ram. This is a 2005 Sony PC with 64 bit dual core cpus running W/8 64 bit, but the mobo will not use more than 3.37 of my 4gb or ram.