If Windows is not able to access the drive or read from it, recovery software will not be able to read from it either. Sometimes it's not the actual hard drive which is faulty, it's a faulty interface converter board which is in the enclosure. When that happens, your best option is to remove the drive from it's enclosure and put it inside a new, third-party enclosure which you can buy at most large computer stores. But if the drive itself has failed even that will not help.
So the first step is to test it in it's existing enclosure.
To test for drive failure, download "Seagate SeaTools for Windows" by clicking "Downloads" on this page: http://www.seagate.com/support/downloads/seatools/
Install it and open it. Tick the external drive and choose the short test. If it fails the short test, you need to buy a new drive.
If it passes the short test, run the "long" test on it just to be sure it's okay.
If the drive has failed, the only way to recover data from it is to send it to a data-recovery service which is very expensive because it requires that the drive be opened and accessed with special equipment.