I'm using a corsair ax860 but it never draws more than 450w from the wall
That seems kind of low for a rig with 4x 1070s, plus everything else.
What did you use to underclock the cards? Something like MSI Afterburner? Or did you do this within Claymore's miner?
Try unplugging the PSU from the wall, wait about 20 seconds, then plug it back in and attempt to boot. If that fails, try swapping out the card in the primary x16 slot and use a different one for your display.