[Recover files from dropped external drive]

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If you dropped the drive while it was reading or writing it is likely that the impact caused the heads to collide with the platter(s) and cause irrepairable damage. The data may not be recoverable if this is the case.

There is no way of knowing if the circuitry in the external case or the HD circuit board has been damaged so the first approach to attempting to recover the data is to either .....

Remove the drive from the external case and hitch it up as a slave drive in a desktop computer - if Windows recognises the drive there is a good chance that you can copy the data off.

The alternative is to install the drive in a new external case and see if it works.

If neither of these two suggestions work there remains the possibility that the hard drive circuit board is damaged - you will neeed to find a hard drive exactly the same right down to the exact model no. and swap the boards.

I would not be at all confident that you will be able to recover any data, but you may strike lucky.

It sounds like you do not have a backup of this irreplaceable data - all personal data whether stored on the computer or on an external drive should be backed up to other external media to cater for unforseen incidents. Many of us backup our backups for added security.