I can’t see any physical damage. The only thing I can do is to help you measure the onboard voltages, but that will most likely just be a post mortem exercise.
If the board turns out not to be economically repairable, then the easiest solution will be to transfer the 8-pin serial flash memory IC at U12 to a replacement PCB. The following PCB suppliers offer a firmware transfer service, either for free, or for US$10:
Otherwise, if you are not adept at soldering, your local TV/AV repair shop should be able to transfer the chip for you.
As for the measurements, you should do these with the board removed from the drive. You should also be very careful, as a slip of your probes can do major damage. Whatever you do, you must not damage U12.
You can start by measuring the voltages on each pin of transistor Q8 (near the bottom right screw hole). I believe these should be +3.9V, +5V, and +3.3V. The latter should be the Vio voltage for the flash memory, Marvell MCU, and SDRAM.
Next measure the voltages on either side of the R050 resistor between L2 and C3, to the right of the MCU, at about 1 o’clock. That should be the Vcore voltage for the MCU.
Lastly, measure the voltage on the anode pin (non-striped end) of Schottky diode D4 (adjacent to L2). This will be the -5V supply for the preamp inside the HDA.
If those voltages are present, then reinstall the PCB, power up the drive, and measure the voltages on each of the four motor terminals immediately after switch-on.
You could use either of the two ground pins in your Molex power connector as your ground reference.