Won't Boot with the Graphics Card Installed

I have a new computer setup that doesn't boot when the graphics card is installed. It begins to start up, but after 1-2 seconds the fans spin down. Then it tries to boot again and cycles like this. There is nothing on the display.

When I pull the graphics card out and run it off the motherboard graphics, it works fine.

System Specs:
ASRock Z77 Extreme3 Socket 1155 Intel Z77 (ftp://174.142.97.10/manual/Z77%20Extreme3.pdf)
Intel Core i5-3450 Quad-Core Socket 1155
Sapphire HD 7770
ADATA SX900 256GB 2.5" 6Gb/s Solid State Drive
I TB HDD
Kingston HyperX Predator 8GB
DVD Burner Drive
Cooler Master 625W Extreme 2
USB Mouse/Keyboard

The power supply was recommended by the guy at Canada Computers as being a safe buy with some capacity to spare. Calculators on the net show that I have the power capacity.

The graphics card was running fine in another system just a few days ago. I have tried it on the motherboard recommended PCIE slot, and a different slot and it acts the same. I have the card power supply properly plugged in and carefully followed all instructions. Connectors have been triple checked to make sure they are properly seated. I can't find any troubleshooting tips for my motherboard.

I have a few things I can try:
- Put the 7770 card into my old motherboard/power supply setup where it was working before and see if it got damaged during the swap.
- Put an older graphics card (without an external power connector) into the above setup
- Upgrade the power supply so I can upgrade to an SLI setup later if I want.
- Use a multimeter to check the card supply voltage as I boot. (not sure I want to do this)

Anyone have any suggestions or things I can check? Any help is much appreciated.