The 5V regulator has problems. Do not trouble shoot with the CPU board attached - may cause more problems as this exceeds the absolute maximum supply voltage for some of the parts.
First thing to look at is the 5V section on the power supply. My first suspects would be the small electrolytic caps C7 and C8.
Once 5V supply is back to normal - CPU board may need a bit more attention.
Battery corrosion seems to have been eating some traces around U41 so the damage may be worse than it appears.