I've never had this bad of a problem on a system 11. ...so I don't know if I'll be much help... But:
How far have you gotten on any diagnosis? Have you done a display test? Have you checked for burnt, corroded or cold solder joints on the pins and connectors? check both the mpu and the display boards? I see 00 on display 1--does it score at all when you play a game?
How bad is the corrosion from the batteries and have you done anything to repair the components affected?
Have you checked any repair guides? (I'm not being facetious, it's something I constantly go back to when I have a problem I haven't dealt with, which is often. ).