Identifying damaged, burnt out, or missing components
Is it possible to deduce the identity of damaged, burnt out, or
  otherwise missing components (or suitable substitutes)?


Without a schematic one can never be sure, but you do have a few clues:



The footprint left on the board is for an (most likely) an SOT-23 package:



This means it was probably a transistor because it has three terminals, but could be any three terminal device. It could be many things.

The easiest way would be to find a working board and find the codes on the top of the device, Here is a guide for identifying components.

The problem with this is even if replaced the problem that led to the failure of this part also could have caused failures in other parts. The traces on the PCB may also be damaged due to the high heat (or high current) of the component failure .