Not a big fan of the Corsair CX due to cheap Chinese made capacitors but yeah it should handle a single HD 7950 fine. Do you by chance have access to another computer you can test the card in? It could very well be a defective card.
Since you tried both PCI-E slots that pretty much rules out a bad motherboard.
Do you have a different power supply you can try?
Your copy of Windows is legit?
Might not hurt to run memtest if the other things don't find a fault. At least 8 hours to test 8GB fully.http://www.memtest.org/