OK - I have removed the apron and checked the switch under the ball and it seems to be working correctly... BUT the ball is not ejecting automatically. If I move the ball into the pin launcher then everything is fine and the system resets and the game goes normally. I tried the self test and the solenoids cycle through but the ball ejector does not work during the cycle. That could be the problem. The switch seems to be new and looks like it's been replaced recently..

Should I test the solenoid with an amp meter?

Also, one of the five drop targets does not drop when going through the test cycle - no sure if that is an issue as they work correctly during play?   

The manual tells you what transistor fires each solenoid.

I am not familiar with Cosmic Princess but it may be a part of the game that you start off with certain targets up and others down, once you hit the ones that are up then it gives you others to hit.

The apron is the steel cover at the bottom of the playfield, the ball launch solenoid and mech is under there.
Take the apron off, check the resistance of the solenoid with your multimeter, if it is under 3 ohms resistance its probably cooked, also check the driver transistor on the solenoid driver board on diode mode with your multimeter, the link I posted will tell you how to do that, compare it against others that you know are working ok.
A visual inspection of the transistor may reveal damage too.