do you know how to wire a car amplifier? if you do then your install will be easier because the procedure for powering your carPC is basically the same (the M2-ATX has the same 12v+, ground, and remote connections as a car amplifier).
you can power your monitor from the M2-ATX's regulated +12v rail (you can splice into a yellow wire from a molex connector). the output rail grounds are the same as the input ground, so you can connect the monitor ground to te chassis.
here is a quick M$paint diagram of your setup. hope this helps you 'visualize' it