As above, not worked on a logic 4 for a while, but if I remember rightly, behind the keyswitch on the board (or keypad on the optima) there is a big resistor. If the battery developed a short or 'dried out' this resistor would heat up to destruction affecting some or all of the 12v outputs.
Check this resistor, see if there are any burn marks on board or obvious signs of heat on resistor.
It can be replaced although to be honest, for the