The HD 6950 and the GTX 560 Ti require a recommended minimum 500 watt PS and two 6 pin PCI-E connectors.
The HD 7970 requires a recommended minimum 500 watt PS and one 6 pin and one 8 pin PCI-E connectors.
The HW1000 has either 6 (in the specs) or 4 (in the manual) 8 pin - 6+2 - PCI-E connectors.
Found on the web....
"The original 6 pin, 75 watt specification was for a minimum current of 2.08 amps for each +12 volt line, hence 75 watts.
3 +12 volt lines x 2.08 amps each = 75 watts.
However, The 6 pin PCI-e power connector is actually capable of handling more than 75 watts.
3 +12 volt wires x 4.16 amps each = 150 watts maximum wattage.
The two black ground wires were added to handle the increased current. "
If there's something wrong with the connection of one or both of the extra ground wires, the 7970 probably can't get enough current, despite you having a 1000 watt PS.
Have you tried different 8 pin connectors ?