Two possible problems I can think of:
1. You have the power and ignition lines swapped.
2. The PSU is overloaded (list your system components and anything else plugged into it)
It sounds more like an overloaded PSU to be honest. The initial load (everything trying to get going) is more than when the system is running.
The fact that it's not turning itself on though sounds like your ignition and power lines are swapped. The motherboard and PSU listen for a change in the circuit (power/no power) and if you have your power wire going to the ignition line on the PSU, it will never see a change, thus never send the signal to the motherboard.