It appears my 2TB Western Digital My Book Essential was knocked around or dropped and now I get a "bad sectors" error. I can read the partition in the drive where the user manuals and setup software are located (shows up as drive M: on my PC) but cannot access the partition (shows up as C: on my PC (my primary hard disk is J:)) where the actual files are located. I got the bad sectors error when I ran the diagnostic software.

I suspect I already know the answer, but if anyone has any creative ideas on how I can recover the files on the drive, I would be most grateful.

Thank you.

You should try to image the disk to another good one.
If you can't, try to recover data with, for example with R-studio.

Then, warranty with the drive.

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if the imaging get stuck, Please stop immidiately and send the drive to the data recovery pros BEFORE it becomes $2000 job!!!

I'll be Black :

"Creative" ideas sometimes coincide with idiot advice , so : the net is plenty of software to try : if the drive doesn't die in your hands, you maybe can get what you need, and... WOW : IT'S FOR FREE.

I'll be serious (not "creative") :

HW imaging with dedicated equipment is "the" option when the drive has suffered mechanical shock like this case AFTER checking head and media condition, disabling some internal features of the drive. This is safe but sadly it's not for free (doesn't cost an arm and a leg anyway).

(Of course if and only if data has at least some importance, otherwise all this discussion is keyboard venting).

1)I think its not usual bad sectors , more likely some head/s was broken becouse : it was knocked around or dropped
2)Notice : Western Digital My Book Essential has Smartware system (internal drive is encrypted) .

So, if you need data, see advice by "BlackSeagaTe" until drive will not be "tortured to death" by someone from amateurs.

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Angel Data Recovery