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