But I don't see what make/model PC so I can't see if this is one of those. Another issue is power. Your post left the full make/model of the PSU so I can't do a basic check.
I just ordered a 970, as an upgrade for my existing build. I took out my old card (AMD 7870) and replaced it with the 970. I made sure it was properly connected to the PCI slot, and that both the 8 and 6 pin power cables were connected. I connected the HDMI cable, powered it on, and sure enough there was no video output at all ("No signal HDMI").
My old card still works with the same cable and monitor, and I even tried uninstalling the old drivers - however there is still no output.
Thanks for reading!