How many watts is your power supply? I ran into something that sounds close on a recent build. When i would put any load to one card it would go black if i went when giving its own power supply not sharing with other cards no black screen, and mining great.
It's 1500 watt thermaltake. I just realized that the issue is specific to the 7970. Even when it's the only card on the pc it won't boot. It works fine in my other pc though. I uninstalled all the video drivers, but still nothing on the video at all when its installed. Not even the bios show up.