It doesn't look like the EL panels are lighting up. If you need help repairing them then check out my tutorial on the Neo forums.
http://www.neo-geo.com/forums/showthread.php?t=198187
It should answer most of your questions. Some people will try to get you to replace the entire EL system with a flourescent fixture. I wouldn't do it. A machine that nice will look good with the EL marquee system working as intended. Besides, the idea of the individual game's marquee lighting up when selected was such a cool idea...