Just wire any old momentary switch to the "power on" header on your atx motherboard.. That's all this is (but with other buttons for reset and leds, that you probably dont need).
This wont turn your monitor on/off. If it was a modern PC monitor, I'd just let it sleep (standby mode) when the cab is off, that's what my PC monitor does (I rarely actually power it off).
You could also short your power header on the motherboard (a momentary short sends a poweron signal, but most I've played with will always power on if shorted), plug everything into a regular power strip, and splice a regular SPST switch onto the hot wire, and let 'er rip.
This wont let your PC "cleanly" shut down, but I'd handle that in software - an industrialized PC (like one in an arcade) should be able to handle a power bounce. It's only a problem if power fails in the middle of a disk write, which shouldnt be an issue on an arcade cab which should do little if any writing to disc, save for hiscore.dat once in a blue..