High odds on the battery leakage being the primary problem. That can be fixed, takes a little continuity checking skill and such but can be done, or you can drop in a replacement and come back to that board later.
For the monitor, start with the HV circuit and go from there, since there is no neck glow or scangun chatter.
And please, please file this away for future reference: you cannot visually tell, with any reliability, when an old fuse is dead. Always always always continuity check them.
You also can't visually check a pinball coil.
Based on that desc, I wouldn't have had much issue with the $200, but I specifically want a Baby Pac.