Even though its a 550 watt unit, there are 3 voltage rails
3.3 volts
5.0 volts
12.0 volts
Very few devices will use the 3.3 or 5 volt rails on a power supply. Its mostly all on the 12 volt rails. That power supply only has 360 watts set aside for the 2 - 12volt rails that unit has. It has a combined wattage of 275 for the 3.3 and 5.0 rails. So basically that unit is crap. How much did you pay for it? Bet you it was around $30-$35 wasn't it? It may have been a little more due to it being a modular unit.
I doubt a new psu will do anything. The motherboard is most likely shot or as I said, there is a short somewhere. I would build the motherboard ouside of the case to verify.