If you are useing this video card
and this power supply.
Then you have a POS 400W PSU (on its best day) thats rated at a PEAK output of 520W. And a continous claimed output of 400W. Which is still short of the recommended specifications of said video card. (And highly doubtful it even delievers that much reliably.)
And of course you won't have a problem with intergrated graphics seeing as how they use very little power hince why they are so weak compaired to dedicated cards to begin with. (not to mention the A6 intergrated graphics are a joke when compaired to the 7700 series)
A 7770 series uses more power then the A6 in your PC.
I5 3570K@4~5.0ghz: Gigabyte GA-Z77X-UD3H:Corsair Hydro H110 :16GB Corsair Vengeance DDR-3 1600: x2 XFX Radeon 7950 @ 1100/1575 : Corsair AX 860 PSU: x1 WD Black 1TB HDD's: 90GB Agility 3: 960GB SSD : Creative Labs X-FI:Corsair 500R Arctic White Edition:3 22inch Monitors Eyefinity @ 5294x 1050 : Alienware Tact-X Keyboard: Razer Naga :Corsair Vengence 1500 Headset: Corsair SP2500 Speakers