You will need a more powerful PSU.
A 6970 needs about 17 amps, peaking to 21 amps under load. Your CPU will need about 10 amps. And that doesn't include the rest of your system.
A CX430, while a pretty good power supply, only has a 28 amp 12 volt rail.
I would recommend something like an XFX 550 watt PSU:http://www.newegg.com/Product/Product.aspx?Item=N82E16817207013
a little pricey for a 550, but a great power supply and built by Seasonic.
Or one of these:
But my first choice would be the XFX.