Without being able to see a couple of circuit board "landmarks" such as a couple of mounting holes or where a wires connector connects to the circuit board, it will be hard to locate parts relative to the burn mark(s) on the solder side of the circuit board.
However if the oblong solder area in Picture 2 which is marked P2 is the same as the oblong solder area shown in Pictures 1 and 3, I would suspect the black diode with the letter N immediately above the silver band as having blown internally. Actually, I am surprised it did not blow itself apart.
You can test it using an ohm meter - either analog or digital. First unsolder at least one of the wire leads from the circuit board, and then put one test lead from the ohm meter one one lead of the diode and the the other test lead of the ohm meter to the other end of the diode. With the ohm meter set to the, say the X1 position, you should see 0 ohms or an extremely high number of ohms (or infinity). Then switch the test leads around and you should see an extremely high number of ohms (or infinity) or 0 ohms. If you see 0 ohms both ways, then diode is shorted. If you see a high number of ohms (or infinity) both ways, the diode is blown.
Now, if the diode is bad, unsolder the other side of the diode from the circuit board and read the characters printed on the diode. You should see something like 1N4001 or 1N4005 or 1N5401, etc. Those will be the part number of the diode.
Just as an FYI, the 1N4000 series diodes can handle 1 amp of current and the 1N5400 series diodes can handle up to 3 amps of current.
I will say, the electrolytic capacitor located at the bottom of the circuit board in Picture 2 that is bent towards the left, appears to be bulging (I think the capacitor has the letter & number combination of C3 located above it and adjacent to the resistor on the circuit board) is either bad or is going bad due to the bulging. If you unsolder it, the voltage rating and amount of capacitance should be printed on it. Also note is there is a row of minus (-) signs going along one side for positioning.
In the picture I have included I circled the suspect diode in white and the suspicious capacitor in yellow.
Hope this helps and if you need help in finding replacement parts, just let me know the numbers you get off the old parts and I'll be more than happy to point you in the right direction.
Good Luck!