ATX motherboards, as long as their power supply is powered, and attached to the motherboard (and the switch on the power supply is in the "ON" position), indeed are powered. Most of them have some sort of LED on them to indicated that they have power, and some also indicate that they are in standby mode.
The power switches for ATX's are just momentary close, normally open switches. All it does is short the pins, which signals the power supply to turn on. To tun it off, the motherboard sends another signal to the power supply that indicates "turn off now!!" , or you can hold down the same power button for a few seconds, and it will also turn off.
I haven't researched this much, but you might look in the section called "power supplies," they probably talk about good ways for turning them on and off automatically.
If you just want something simple, you could have a relay from your on or accessory switch, and when energized, it will start a timer to close the power button circuit for a short time (half a second), and then open the circuit right after. And of course, when you turn the car off, cut the power to the computer...unless you're running windows or something, in which case you would need to find some shut down controller (again, search in the power supply section) to safely shut down the machine.
Hopefully this will help some.
mobo witout resume on power loss and how power button works
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