On the back of the monitor there is a "flyback" transformer. On one end you see a suction cup, and on the other is a black assembly. On that assembly are two knobs. The one close to the top of the part is the "focus" screen, and the one under it is the "screen". The "screen" is the brightness. If you turn it up or down, then the monitor will get dim. It's kinda hard to reach in one of those cocktails like that, and it looks like it doesn't matter, as the monitor is working.
But if the game is dead when you are sure you have the +5 and +12 volts on the game, it sounds to me like your board is dead. If you are savvy, there are some basic trouble shooting things you can do to fix that.
Why? I am not sure. Most of the time something happens to the power supplies, and when that happens, the boards get a surge or don't have enough power to function. Usually you can tell because you will see at least garbage when you turn the game on and off. But you have power.
Try this, just for the sake of it. Find your +5 VDC, then flip your meter to AC. You should see no more than .5VAC on that. Try it on the +12V DC portion too. If you see more that .5VAC, then one of the caps failed in that power supply and you have too much AC "ripple". That may tell you why it failed. Whatever is in there can be replaced with a new switching power supply for about $30.
Keep in mind that game is very old. It's from 1985. I had a game called "Atomic Punk 2" that died and when I decided to check, the capacitors had rotted off the board! They leaked all over the chips and shorted one out. Perhaps one of the 7805's on the board decided to give out and the board isn't powered, or whatever.
If you don't have a manual, and you want more info on the game check this link.
http://www.arcade-museum.com/game_detail.php?game_id=8221If you find the PS is okay, and you really like the game, my advice is to just buy another board for it on ebay. I noticed in the klov listing link that there are parts for it.
If you want to jump in and try and fix it, here's where to start
http://forums.arcade-museum.com/showthread.php?t=177192