When a drive shows up in Disk Management and isn't making any noise, you're in the realm where read-only software will work. On the other hand, if it is silent, clicks, or just comes and goes, you are not, and the distinction is way more important than any tool.
You can always copy from, image and scan the drive with read-only tools without making the situation worse; however, formatting, running chkdsk, initialising and loading recovery software onto the drive itself can and frequently do harm.
The main components of an external hard drive are the disk itself, a bridge board (converts the disk to USB), and a power source. The two non-disk parts of an external hard drive are responsible for a large share of its failures, and therefore many times an undetected external hard drive has a working disk inside dead electronics.
Most of the diagnostic effort in determining what has gone wrong with your drive is simply identifying what part(s) have failed. Several of these tests are free.
Warning before you start, because this is the expensive mistake: don't remove your drive from its case until it has been assessed.
WD My Passport and My Book encrypt at the bridge. Your data will remain encrypted on your hard disk, and the encryption key will be stored on the bridge board. If you remove the disk from its enclosure, Windows will see this as an unformatted device and ask for permission to initialise it.
Seagate and Toshiba are usually simpler. The majority of Seagate and Toshiba cases don't encrypt their disks; therefore, if the disk in one of these devices is still working, it can often be read directly. Even so, you should always ship the entire enclosure (case) rather than just the hard disk itself.
If it is already out, keep the case. Don't dispose of any of the individual components in the case (circuit board, cable, power supply), even if they look dead. These could prove critical if your device uses an encrypting circuit board, making the difference between a routine recovery and an impossible one.
Test the power supply on desktop units. 3.5-inch external hard drives use a separate AC mains adapter. This AC adapter fails more often than the drive it powers.
Try two cables, a rear port and another machine to see if you can get something out of it, rather than accepting it is dead. It is more common to find failed bridge boards or sockets than mechanical failure.
Decline. That error message indicates that the file system cannot be accessed and may indicate a failure with the bridge or, if it's been taken out of its case, an encrypted disk.
Not until after we have assessed the problem, and never on Western Digital's My Passport or My Book. Send us the entire unit, cable and PSU included.
Costs will vary but start from £300 +VAT, and the price is fixed after a free diagnostic test. The cost of dealing with a bridge fault is usually relatively low as there is no need to open the drive.