Take a look thorugh the galaxian trouble shooting guides. The first thing I do with a galaxian board is replace all the socket and clean the roms then go from there. The roms almost always have rotted pins but they tend to break when you pull them so beware.
It's looking like chip 2B, I just tested the outputs on it on a board with this problem (fast random moving star pattern with too many stars) and there are no outputs from the 74 366 chip when tested against a known good working board.
I'm going to order a replacement and replace the chip - let you know what happens.
Are you using it with factory power supply or switcher. I was running mine on a test bench with a switcher and voltage was 4.6 I upped the voltage to 5.1 and problem went away