The computer power supply will require a minimum load to be present before it will power on, and you need to determine which of the power supply pins controls the power to the system. Typically the motherboard of the computer does this. (remember that the power switch on a computer is not connected to the power supply, but is attached to the motherboard)
I'm not sure which pins carry the 3.3V or the power-on signal but it should be fairly easy to figure out. You have to do something to those pins to get the power supply to work. The below links may help.
I found these with a Google search: atx power supply 3.3 volt pin