^+1. As long as the PSU isn't junk (i.e. really only a 200W unit), you should be fine with a HD6670. If it is a Dell, Compaq, or HP, you're probably good; if eMachines, likely not (especially if the PSU is by Bestec). Can you tell from the label who made the PSU?
I have a HP computer and on the psu it says delta electronics. So would a 6670 be ok then?