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.