For a system using a single Radeon HD 6970 graphics card AMD specifies a minimum of a 550 Watt or greater system power supply. The power supply should also have a maximum combined +12 Volt continuous current rating of 32 Amps or greater and have at least one 6-pin and one 8-pin PCI Express supplementary power connectors. AMD's power supply requirements are based on a PC configured with an Intel Core i7 3.2GHz 130W TDP processor. If we base it on your Intel Core2 Duo E7600 (Wolfdale) processor then the power supply's recommended maximum combined +12 Volt continuous current rating should be 27 Amps or greater.
Total Power Supply Wattage is NOT the crucial factor in power supply selection!!! Sufficient Total Combined Continuous Power/Current Available on the +12V Rail(s) rated at 45°C - 50°C ambient temperature, is the most critical factor.
Overclocking of the CPU and/or GPU(s) will require an additional increase to the maximum combined +12 Volt continuous current ratings, recommended above, to meet the increase in power required for the overclock. The additional amount required will depend on the magnitude of the overclock being attempted.
You may find power supplies on the market that supply more than enough Wattage to run the system. However, some of them lack Sufficient Amperage capacity on the critical +12 Volt rail, which is necessary to properly power the critical components in the system (i.e. CPU and GPUs). This is the reason why graphics card manufacturers may overstate the power supply wattage, usually by at least 50 Watts, in an attempt to take into account some of those power supplies that have the weaker +12 Volt rail(s).
The HKC Silent Series 550W (USP-5550) (assuming you're using this model since you never specified the model number), with its maximum combined +12 Volt continuous current rating of 24 Amps and with one 6-pin and one (6+2)-pin PCI Express supplementary power connectors, is insufficient to power your system configuration with a single Radeon HD 6970 graphics card.
There's a good chance that you're triggering the power supply's overload detection circuit. This will cause the power supply to turn itself off unexpectedly.
Get a better quality power supply unit with the proper specifications from a reputable brand like Antec, Corsair, Enermax, Seasonic or XFX. Stay away from the generic budget PSUs like HKC.