What is the model number of the TV? I have access to some Sharp service manuals which may or may not help.
What is the model number of the WD external drive? Is it a My Book Essentials or an Elements? The former is encrypted whereas the latter is not.
Do you have a cheap USB flash drive that you could experiment with? If so, does the TV also lock this drive?
You say that you "would like to avoid formatting" and that you are "desperate to get all this data back", so why are you attempting to write to your drive? Are you not aware that initialising your drive is data destructive?
That said, it does appear that your TV may have password protected your drive for DRM reasons. If so, and if the user manual does not warn you that this may happen, I would suggest that you pursue a remedy via your local consumer protection body.
Otherwise, how do HDDScan or HD Sentinel detect your drive? Do they show the drive's Security status, and is it locked? If so, then you can remove the drive from its enclosure and work on it while it is connected to a SATA port on your computer's motherboard. Let us know if you get this far.