To fix the burn in the circuit board you have to have a soldering gun, flux paste, tin- lead and good soldering skills. To repair , first you have to find the area that has the open circuit, then remove the green material that protects the cooper for corrosion. Put a bit of flux paste on the expossed part of the circuit that we previously peel. Then solder the area putting a bit of tin-lead. Find a piece of wire (small caliber..18-24 gauge)to make a bridge in the 2 areas.
Check the wires and contact of the batteries. If all are good. Check polarity of batteries. If all is good. A tiny line of the circuit board is burnt because you put the batteries in a wrong way And there is no fuse.
First of all you have to have good soft solder skills with thin. Find all screws. Specially the ones of the microphone. You have to dissasemble the shutter board from the main board. You will have to remove the solders. Are 12 or so. The main lens flex connector is a PITA. Takes around 1 to 2 hours to fix it. The lock of the sd card switch is bent all the time. Reshape it to the original position very careful. Is tiny.