If you swapped out the video card for one that worked that takes less power, that confirms my thought that it is the power supply.
Apevia is just not a quality supply and that is common with supplies that are not quality built. While that Apevia is listed as a 620 power supply, you may not be getting more than 500 watts out of it when you factor in everything.
You need to be up here to run this video card:
http://www.newegg.com/Product/Produc...82E16817139005
Note: Some times you can even find a Corsair 750 for about the same price, but I did not have time to check that one. Might be worth looking on NewEgg and checking. Also, if you purchased this recently, see if you can send it back and swap it for a decent power supply.