System won't boot: Gigabyte HD 7790 1GB OC GPU issue or Corsair VS550 PSU issue?
I've seen that problem happen before with a brand new graphics card with 2GB of RAM. The graphics card worked fine on one computer, and the other computer wouldn't start with the new graphics card installed in it. The fans would spin, but there was no monitor signal at all, neither for VGA nor HDMI.
The first thing I would check to troubleshoot your problem is your ASRock motherboard1. Maybe your motherboard isn't delivering enough power to your graphics card. A graphics card with two large fans like yours would require more power than usual when the system is booting.
1 Motherboard BIOS update fixed it.