Hello and thank you for choosing JustAnswer.
External Hard Drives are enclosed in a plastic enclosure, which has 2 components.
1- Power convertor
2- USB to SATA convertor board
So, if the the Hard drive WONT recognize through the USB port on your computer, you can (only for the technically savy) remove the hard drive from its enclosure, and remove all the internal components, leaving ONLY the bare hard drive, and then connecting it INTERNALLY to a desktop PC.
The USB board might have failed inside the enclosure which would prevent the drive from being recognized by your computer when you plug it into the USB port.
The Power convertor might have failed inside the enclosure too.
By hooking up the bare hard drive (after you remove it from the enclosure)to a desktop PC internally, you will be bypassing the possibly faulty components. The USB board, and power convertor.
Now, if the hard drive STILL wont spin up, and be recognized....then the drive is DEAD, and ONLY forensic drive experts can recover the data.