The simple starter tests are this:
1. You open up the back and look for dangling wires and anything that looks disconnected or "wrong".
2. If all looks safely connected, close the back door, plug it in and power on, at which point you look for:
A. An image on the monitor
B. If no image do you hear that typical high pitched "whine" like TVs make?
C. Open coin door and flip the coin switch. Did you hear sound?
If you hear sound but no image, then something is wrong with the monitor or the connection to the monitor. If the monitor sounds like it works, but you get no game sounds, then the game board is not connected properly or is broken. (Another monitor test is to look at it from the back and check for an orange glow in the neck of the tube).
If the monitor works, and the game board is hooked up correctly, sometimes you'll still get an image. It will either look like "junk", scrambled lines, or will be a report stating that RAM or ROM has failed.
BTW, don't leave the machine on for too long when doing the above inspections if you are getting no picture.
3. Check the fuses.
Where to go from here depends on the symptoms.
~Ray B.
PS: does it look like this:
http://www.klov.com/game_detail.php?letter=&game_id=10503