Dryer does not turn on with button push, but will run cycle randomly

As per the title, the dryer (Maytag Centennial) doesn’t turn on when pressing the button, but will turn on randomly if the dial is left on a cooldown cycle.

I have already tested the thermal fuse, start switch, and door switch with a multimeter and all appear to be conducting as expected. The start switch has 3 prongs, 2 of which that conduct regardless of the button press, and a third that conducts only on button press.

Given that it does turn on (and the drum does turn on when it does), I expect the issue is not the motor or belt - but instead the main board or timer. Is there an efficient way to troubleshoot those components? And a way to repair without replacement?