The following companies I would suggest: Drive Savers Salvage Data We Recover Data
If this is a WD external, removing it from its enclosure is not advised. WD drives in enclosures are SED (Self Encrypting Drives) and require special tools to recover the encryption key for data and surface area access. Hopefuly the drive is not in too bad a shape.
If sending out for data recovery, the 3 companies above do the following:
1) No data no charge (Salvage Data sometimes has an attempt fee depending on dificulty, but this is rare. Not sure if policy has changed since I worked there...)
2) Free diagnostics and quote
3) I know drive savers doesn't charge for shipping. I cannot remember if the others do as well.
4) They offer financing when needed. Data will not be sent till debt is paid.
For a recovery expect to pay between $400-$2000. In rare cases, it can be more. Generally, the longer you are willing wait, the less you pay. The only way to know for sure what the cost is is to send it out. Again, no charge. If you say no, not an issue. They will just ship the drive back.
Also, DO NOT OPEN THE DRIVE UP! DATA RECOVERY COMPANIES HATE THAT!!!!!! They will usually charge a previously opened drive fee. Some will downright decline the job. Furthermore, you risk your data if you do!
If you live in the US, these companies will also do free shipping both ways if I recall correctly. Either way, not a bad deal. I know drive savers ships you a box, you put your drive in, ship it back.