I just finished up an Omega Race myself... I think its a great game.. wasn't all that popular in the day tho...
Anyway, you might not have a monitor problem. Is there any sign of life in the beast ?? Game sounds, coins up ? Start button light blinks when you add a credit ??
If there isn't any indication that the game board is working, check ALL the voltages at the board connectors. There are several different voltages the board requires. A quick google search should net you either a manual or at least a pinout chart for the main and daughter boards.
If voltages are present, and there is no sign of game life, you probably have a board problem. Those can be very tricky to troubleshoot.
If the game does appear to play, but the monitor is just showing a dot, you've got monitor problems. I'd need to know which monitor your game has (a G05-80x I'd guess). First check ALL the fuses on the monitor chassis, there are several. You see a white dot, that's good, it means the high voltage unit is working, although the spot killer should have prevented the dot, it's still a good sign.
D