Did you install everything correctly, make sure your psu was correctly installed and try with your old graphics card, or if you have integrated graphics make sure you have your hd 6670 unplugged and see if it works. If it works, then uninstall your drivers and then install your hd6670 in a pcie slot either x8 or x16 is fine. The hd6670 is a low profile card so you don't need any additional connectors for it, it simply draws power from from the pcie slot. After you have inserted the card and you log into windows install the drivers from the included CD or download them online.
Hope this helps!
Yeah my PSU is installed correctly and my old graphics card works fine and my integrated graphics card also. When I install the 6670 my computer monitor remains black and blank.