For what it's worth, I dropped a GT520 PCI-E card into the box to see if that would fix the problem - no dice. Against my better judgment I re-seated the memory chips even though they had past post-test and again, no luck.
The mobo seems incapable of producing a video signal when paired up with an A6-3500. So I say "Boo! Gigabyte, Boo!".