That's a VIA HD Audio chipset and a real problem with Windows 10.
You could try the Windows 7 driver that they offered to email you and see if it works depending on the contents of the driver package you may have to install it in compatibility mode if has a "Setup.exe" program.
I went through this same deal with a buddy in North Carolina (BassFisher6522 he's a member on this forum).
I don't recall for sure, but I don't think he ever got it resolved and I believe ended up going back to Windows 8.1 if I'm not mistaken.
Another option might be to shop around for a cheap add-in card, depending on what slots you might have available.
When my integrated sound went out on my Gigabyte board I bought one of these
http://smile.amazon.com/Creative-So...566&sr=8-1&keywords=creative+sound+blaster+se
Seems to work fine on this Windows 10 Pro 64 bit machine I'm using now.
I disabled the integrated sound in the BIOS, that may be an option for you.... if you have an open PCI slot.