You most definitely need a wring diagram and if possible circuit description. It would seem that the starter is permanently energised, which is why, in all likelihood the the main wiring has burnt out. Disconnect the starter main wiring and then, after replacing all the burnt out wiring and charging the batteries see if everything is normal.
It is usual to have a wire from a starter button/starter switch that energises a solenoid, either remote from the starter or built into the starter itself, that appears to be either permanently energised OR its contacts are short circuit.
Be aware that the main power cables to the starter are normally, when the main isolator switch is on, at full battery voltage and hence current, with no fuse. A short circuit here may even cause the batteries to explode, apart from cooking the wiring as you have discovered.
Diana