There may be a misunderstanding here. The "Power on" connection of the power supply is not the same as the button on the front of the computer.The power supply will operate only as long as the "Power on" connection remains connected to ground.A paper clip is not an appropriate means to do this.
You probably need a higher minimum current than the 10 mA with a 470 Ohm resistor, try a 47, 106 mA, and you may need minimum loads on the other outputs.What does the supply's documentation say?
In your link, Step 5 won't work, Step 5: Solder on Your Dc Jack for Arduino Power. Using thet DC connector with an Arduino you need to apply > 7.0 volts actually applying an external 7 to 9 volts is ideal and 7 to 12 will work but remember what you apply on that connector is applied to the Arduino 5.0 volt onboard regulator. Ron
Ah ok, so I should hook up the arduino to the 12v out?