This is going to sound very dumb, but I one time fixed a hard drive clicking problem where my disk was not reading properly, by turning my computer (or in your case your external hard drive) upside down. This seemed to re-seat the needle head onto the disk, and my computer has worked great ever since.
I originally laughed my friend off for giving me this absurd suggestion of turning my computer upside down so that it would turn on, but it worked, and I owed him a solid thank you. :) It's a very slight chance, but you never know.