First of all, I need to know which pins should I short to turn on the PC.

I opened case and checked pin assignments by measuring voltage and resistance.
Result is in the following picture:

First pin, left most one, outputs 3.3V even if system is shut down. This seems to powering LED.
Second pin is connected to ground.
Third is the one I need. Shorting it to ground turns on the PC.
Forth pin controls the LED. Shorting it to ground turns on the LED.
In the other words, outer pins are for LED, inner pins are for switch.

It turned out there is everything I need: power, ground and switch. Additionaly, I may be able to use LED control pin to detect whether PC is on or off.
I don't know how much power I can draw from the 3.3V source, but it is unlikely to hurt anything if I draw a few milliamperes.