For sure that Corsair PSU is able to feed this internally crossfired double card.
The connector I mentioned is that one black eight-pin in the picture below. It should be connected to the PSU and I think that Corsair PSU have the appropriate cable and plug. Otherwise, a special cable is supplied with the card and it can be plugged in one of HD drive power supply wires.
Without that 12v there will be no video.