Car amp burned out component
The brown squares are ceramic capacitors. Judging from the photo and your analysis that it was a brown square, the burnt component was an input filter capacitor for a switch mode DC/DC converter.
Without a service manual to provide schematics or a component list, it is impossible to determine what will be a suitable replacement capacitor.
There is also a lot of PCB damage, the conductors are burnt off so there is nothing left to solder the capacitor.