Just read 13 pages of what happens to be the same problem I was having. I have the answer to your problem: it’s the way it’s connected. I have a WD Passport Essential 250GB. When I plug it into any computer, it makes a clicking sound like the old computers of 12 years ago did. The light is on as well. If your WD Passport HD is doing the same thing and not being recognized by your computer, simply push the USB cable connection harder into the WD. It’s a power issue. It’s the copper connector and after plugging and unplugging, you are wearing away the copper. I bought mine 2 1/2 years ago and will be replacing mine since it’s under warranty.
I just got it to be recognized by pushing harder until the clicking stopped. Just finished backing it up onto my desktop.
So your data is most likely safe as well as the hard drive. No need to send it to a data restorer company.
Best of luck,