I've been playing around with an Arduino as well this last week or so. They are very clever. To turn the Car PC on, all you need is to trigger a relay in the accessory line that turns on your PC power supply and maybe a sensor on the ignition line so if the engine is on, you don't kill the Car PC as there is no load on the battery.
Another alternative is to sense the battery voltage with one of the analog pins thorugh a voltage divider and if it falls below say 13 volts (eg. Alternator is not charging) allow the Arduino to shut down if the BT signal is lost.
To sense 12 volt voltage, feed the 12v input to a relay (maybe a solid state one) on the input side and switch 5 volts on the Arduino onto the input pin you are using.
I've started to put some stuff together from my car PC
These ar Solid state relays, 2 amps 3-50 volt DC. There are 4 input relays and 4 output relays on this board I will be using. There are two kinds of relays here. One lot handles a 12 volt input (which will be inputs to the Arduino), the other handles 5 volt input (which will be outputs to the Arduino)
I've also got some smaller ones that can switch at < 3 volts.
The LED's represent the buttons on my monitor and when reversing lights are sensed, the Arduino will press buttons to switch inputs. The press button switch represents the reversing light switch. I have put stuff about this on my worklog and the first cut code for the monitor is there.
I will also make the Arduino work as a temperature sensor for RR. I have tested this and it works!