I located the two pins that are responsible for powering up the PC. The are connected to the Power On button and one pin has an output of 5V while the other is the ground.
So far so good, the problem is when I connect the 5V one to the Ardunio VIN and a ground cable from the PC power source to the Arduino GND, instead of powering my board, the PC starts and then promptly stops, as if I pressed the power button and did not release it.
It seems that electricity passes through the Arduino without powering it. I tested the VIN and GND pins with a normal breadboard power source and they are not broken, as the board starts up with no problem.
My plan was to power the Arduino with the 5V pin and send a digitalWrite(somePin, HIGH) for a short amount of time to the ground pin from the PC that would normally be connected to the power button, thus "closing" the circuit like the normal case button would.
It /sounds/ like you want to power the Arduino from the power-signal-pin - that won't work.
To power the Arduino, connect 5V from the PC's standby-supply to 5V-pin on the Arduino - not VIN - VIN Needs approximately 7.5V or higher to work properly.
To "press" the power button, alternate the pin between being an input (not 'pressing' the button) and then an output and low, then 'pressing' the button.
The super awesome way to do this would to be using an optoisolator (look it up!) and use that for "pressing" the button - it's a safe way and you don't end up destroying anything by accident.
Ok, I understand that I can not power the Arduino from the signal pin.
I connected it to the 5v and GND of a on-board USB set of pins.
But if I connect the POWER ON pin which does not have voltage to the USB 5V pin, the computer will still not start. I'm guessing connecting it to an Arduino pin and using digitalWrite(HIGH) would be similar.