Which model of drive is it? With the WD external drives, almost all of them encrypt the data between the USB bridge and the platters, making it much more complicated for DIY recovery attempts. That said, assuming that you are referring to a MyBook, you can try the following, with the understanding that if the issue is with the drive, itself, every time you power it on, it could be causing more damage.
1. Try different power and USB cable
2. Remove the drive from the computer (if it detects the drive, it will likely not see the file system because of the encryption)
3. Connect the drive to a new USB bridge with the same part number
4. Try accessing the drive with a data recovery program, such as
R-Studio, and see if you can find your files with it (Again, if the drive is failing, running any data recovery software will likely cause more damage to the drive)
The odds are, you will likely need the assistance of a data recovery professional. So, assuming that your data is worth a few hundred bucks, you may want to contact a few labs to find out what kind of price you can expect. A few labs I recommend are as follows:
Recovery Force
Data Medics
Data Savers
PC Image
Data Busters
This list is far from complete. It is just a few labs that I know who are really good at what they do and because they don't have huge sales and marketing teams, they have considerably better pricing than most labs.
Good luck