This all depends on the nature of the 'failure'
If the device is spinning but the data is inaccessible then this software may access it - but it will cost about £20 or so for a fully functioning copy.A trial is free- but wont save.
Bad Copy Pro from click here
If it is mechanically dead then it is dead.
Another way is to try it on another machine - it after all may be nothing more than a USB glitch.
A free alternative is to put the whole shebang in a freezer overnight and then hook it up to see what happens- has been known to work.
Do report back what happens.