If it is out of warranty open it up.
It is just a normal hard disk inside, plug it into the PC directly if it is a 3.5 (Desktop) (for 2.5 you need a converter/Laptop) and see if you have the same problem.
But you should do this until you tried changing cables and other computers.
Also you should try plugging it in the back as the USB provides more power.
It sounds more like the external device's controller is dead or the hard disk controller.
If you have some other software, check the SMART.
If your BIOS is able to disable SMART, disable it cause SMART might be "stucked" cause it is waiting for the drive to respond.