If you have your drivers installed correctly and you have set the multiple display options to "extend" the desktop (not duplicate), then you should get an image straight away on both monitors.
If it was a resolution problem, you would get a flickering screen, not no screen. If you have the 75ohm / 1kohm switch set wrong, then perhaps your image is too dark to see. Try adjusting the contract and brightness pots to full on the remote board to see if you get an image.
The most likely cause of your set-up not working are: driver not properly installed, broken arcade VGA card, broken VGA cable or broken monitor. I have the same hardware and it is pretty much plug in and play once the arcade VGA drivers are installed (this can be annoyingly problematic sometimes).
Start by testing your components one by one with other hardware.