MSI Afterburner doesn't reflect a 1070 - just says Internal Graphics. Same with Device Manager.
My 1070's led's are lit, and fans running.
This suggests the problem is not power. I also assume if the power connector is labelled for a specific slot
you only need to connect power for populated slots.
Test with a known working GPU if you have one or test the 1070 in a different system to prove it works.
Try a known working card in another slot in case you have one bad slot.