Hey there, Phil!
I'm sorry to hear about your WD My Book.
I'd suggest you to test your external drive with Data LifeGuard Diagnostics.
Run the extended test, it will let you know what's the health status of the drive.
Here's a link to the software: http://products.wdc.com/support/kb.ashx?id=HMUTp1
Can you please share a screenshot of your Disk management, so we can see how the drive appears there and be more helpful?
Another thing you can try for troubleshooting is to uninstall all the drivers under Universal Serial Bus controllers in Device manager.
Afterwards restart your computer, wait until Windows updates reinstall the drivers and try to plug the WD My Book again, see if that would help.
Keep me posted with the results. Hope this helps.