If at all possible, test the graphics card in another computer to make sure it's functional. Make sure that computer does have a power supply with a 6-pin PCIE power cable. If that works, we know it's not the card.
Next, if at all possible, temporarily borrow that power supply and put it into your computer. Test to make sure that installed in your computer/motherboard and with the 6-pin PCIE power connection, that it works. If it works, this eliminates the motherboard as the issue and you now know you need to replace the power supply. If it still doesn't work, then the issue is with your motherboard's PCI-Ex16 expansion slot.
-Wolf sends