OK that's a good start.
To really understand the design, I would need a complete schematic diagram of the PCB and the off-board components it connects to. The ICs need to be represented as rectangles, apart from the LM324 which needs to be represented as four op-amp symbols (see the data sheet for the pin allocation). Generally this requires multiple passes, gradually refining the schematic from a "this connects to this" diagram to a drawing that really shows the function of each part of the circuit. This is a fair bit of work for you, and I don't know whether you'll be prepared to do it.
Also, I'm interested in the voltage rail on pins 8 and 4 of the 555. This rail is tied in with the resistor that lost its smoke, and with the connection between the remote start switch and the LM3524 shutdown pin. Can you make sure that you draw every component connected to that rail? Is there a zener diode connected between that rail and the 0V rail, to regulate that rail voltage? I suspect the resistor that lost its smoke was a much lower value than 330R. What voltage do you measure on that rail now?
The photos are reasonable quality but I would like to see both sides, with views directly downwards on the board or at a slight angle, and with the board square in the frame.