OK basically to answer your questions, not likely to get a resolution with out opening the computer as well as the external case. Based on your description, there are two possibilities,
1) a fuse or protection in the external drives power supply circuit. There may or may not be one.
2) The TVS ( transient voltage surpressor diode ) on the PCB of the hard drive itself inside the external case.
In either case, you will have to open the external case to get the HD out. The TVS will be a diode located near the power connector. if you heard a pop, and it was the TVS it will probably be obviously damaged by the overvoltage. If you identify the blown TVS, then you can remove the TVS from teh board with a soldering iron and solder wick. This will allow the drive to function BUT IT SHOULD ONLY BE USED TO RECOVER YOUR DATA TO ANOTHER DRIVE in this state! Once you remove the TVS there is no longer any protection on that line ( there are two TVS one for 5 v one for 12 v ) and the next surge will hit the more complex and expensive components.
Now it could be a fuse or TVS on the extrnal housings board too, but my experience is it is usually the TVS on the drive. You won't hear naything from the drive except the pop of the TVS, when the TVS clamps or does it's thing to protect from the overvoltage, it will show a short in both directions using a VOM.
Once you have the drive itself physically functioning, you will need to connect it to the PC, which will mean opening it to recover the files you need, and you will need another drive to recover those too. Recovering to the same drive could overwrite data you want to recover; destroying that data. If you can find a comparable TVS based on teh numbers on the diode, then you could replace the TVS and the drive should be protected, but even tho the TVS did it's job, the preamp or other circuits could have been hit with some overvoltage and may eventually fail.
Wish there was an easy fix for this, but unfortunately there isn't a magic software bullet...