Great intro Ric, and I'm pleased you are back in the hobby ! Don't let these minor issues get in the way of enjoying the games again.
Galaxy - When you say "ball kicker" you mean the outhole that serves the ball into the ball trough ? There's a "self test" button in the door. One of the white buttons is the "self test" and you can cycle through the tests until you find the solenoid test. You will know it when you start hearing each solenoid activate (I think the first is the lights, then displays cycling through and then the solenoid test). Now if the "ball kicker" solenoid fires, then you know you have a switch issue.
Galaga - Screen is messed up. Reseat the connector to the board. Test the +5V on the power supply or at the edge connector. Do you have a pinout diagram to determine which pin the +5 V is ? Is it a Jamma board ?
Sega with horizontal bars - reseat thew edge connector. Check the +5 Volts. Reseat the eproms.
There's a start !
