yes you do need a new psu if you want anything more powerful than a 5670 or 6670. it only has 22A on the +12 and thats 264 watts for basically the whole system. You'd want about 350 watts to run a good card. It will still be a good upgrade if you don't expect max settings in games.
if you want a more powerful card, you probably want a new quality 400 watt psu with a 6850, this can be had for about $180.
Can this handle these game GTS 450 1024MB?