It could be booting with resolution too high for the monitor.
Try tapping F8 on boot and selecting safe 640x480 graphics mode on boot.
If that fails, go into safemode, remove drivers then reinstall in normal mode.
I tried that and to no avail. I even tried connecting it to my HDTV, but it still would not give me the windows login screen.
Could it be that there is damage to either the card or the PCI 3.0 slot on the motherboard?
I put the 7870 into the PCI 2 slot and it all works like a dream. Should I RMA the motherboard?