|Make sure all the cards are completely in their slots--especially video. Sometimes when you're inside the case one will work itself loose and you won't notice it.|
If the PSU has a 110/220 voltage switch make sure it's in the correct position. DON'T GUESS. And only change the switch when the power cord is removed.
If that's not it put the old PSU back in and see if it works then. If not--and you're sure everything's connected right--then likely the motherboard or something attached to it is damaged. In that case temporarily disconnect all the drives and remove all the cards except video and try it again.