Use a J-Pac & Arcade VGA to interface the PC to the Arcade Machine...
The use some sort of vieo capture card/USB device to display anything you want through a full-screen viewer on your PC.
To use the Composite input, turn on your PC, hook up your other device to the Composite "IN" jack on your selected video input device on the PC, Start up the video device's software in full-screen mode & play away!
I know I'm simplifying things a bit, but this is would be a viable route... Although it will cost 2-3 hundred for the hardware (J-PAC, Arcade VGA, & Video capture device)
Good Luck!
- tmasman