This sounds like your graphics card is defective.
You need to test it in another system which has a PSU with sufficient 24V amperage for that card. I think it's 38Amps. Most 650W or higher PSU's should be sufficient.
If it's a dual-rail system the Amps will be shown as a combined value; you can check this information online, in the manual or on the PSU itself.
I'm about 95% sure it's a bad card.
You can also contact the company that sold you the card assuming it's still under Warranty. If it's under Warranty initiate an RMA or simply contact support and explain the problem, though I'm certain they'll tell you to return the card.
A less reliable test is to try a different graphics card. To do so:
1. Remove the video drivers (add/remove programs)
2. Shut off your PC
3. Switch graphics cards
4. Turn on your PC
5. Install the drivers for the new card