Adding the GTX 1070 is what made me ask about the power supply. Maybe that card requires more power than the one it replaced? Now a 2nd one is dead, so something is definitely wrong. Are you running with the onboard video for now?

Without a sophisticated++- PSU tester it's difficult to test them unless it's just not putting out a voltage, which is not your case at all. If anything, I would expect one of the voltages that feeds the GTX 1070 is low or fluctuating. The only way to test for sure is replace it.