The behavior of the power button is dependant upon the motherboard you use.
This is not important.
I assume you are wanting to power on the PC when you disarm the alarm?
If that's all you are trying to do, you will need a relay. If you have an AUX output that can be used when disarming, use the relay there. If not, you might have to hook inline with the alarm speaker. If you do this, you will probably lose 1 half second of the sound it makes. It all depends on the relay you use.
Now to hook to the motherboard, you would take off the power connector on the board, and put the open switch of the relay there. When you hit to disarm, it will power on. If you hit to arm, it will power off, and depending on your OS, and power configuration (inverter directly to battery) it might even shut down.
If this is not what you are talking about, sorry....