Go buy a sub $10 DMM at Radio Shack or Harbor Freight or someplace.
They are easy to learn to use, you won't kill yourself. Most importantly, it's the only way you are going to be able to figure out what is wrong short of just buying a bunch of new and expensive boards.
The fact that a known, good working display is also dark on your LW3 almost guarantees it's a power problem. You need a DMM to figure out if you are getting operating voltages sent to the display controller.
You said you swapped DMD's, so I assume you have a compatible game? If so, swap power supplies and see what happens (though be aware Data East went thru several different versions, so make certain it is compatible).