When switching the game on, it may buzz and not appear to self-test at all. Some interference may be displayed on the monitor as well, but there's clearly not a signal, and the game is unresponsive. Test mode will not provide any error beeps.
If this happens, and your power supply is otherwise good, it is likely the clock portion of the PCB that has started to fail and should be examined. It consists of a hex inverter (74S04 series), 18.432MHz crystal, two 330ohm resistors, and two 100pf mica capacitors. The two most likely to fail components in this list are probably the 74S04 or the 18.432MHz crystal, so both of those might as well be replaced.
This circuit is what generates the clock for the game, so if it is not working, nothing else will, either. If you have a scope handy, the 18MHz test point will quickly show if it is working or not.