I have a 1Tb Samsung Story external drive which I use to backup my Mac. The drive is plugged in almost all the time but only powers up when the Mac initiates a backup. As of yesterday the Samsung won't power up and the Mac can't see it. It's not a power-supply problem per se, because when I disconnect the drive and reconnect it the drive starts to spin up and the glow-light comes on, but this only lasts 2 or 3 seconds and then it dies again. I wondered if it was the USB connection that had failed so I swapped my USB peripherals around to different connection sockets. The other peripherals still worked, the Samsung didn't.

An external disk-drive has four major components:

* the USB cable,

* an "internal" disk-drive inside the enclosure,

* a USB-to-disk-drive adapter inside the enclosure.

* a power-supply (only if the disk-drive is a "desktop" drive;
a "laptop" disk-drive gets enough power through the USB cable)

So,

* change the USB cable,

* try connecting to a different USB port,

* try connecting to a different computer,

* disassemble the enclosure, and remove the disk-drive.
Temporarily connect it as a "slave" disk-drive into a desktop computer, to see if bypassing that adapter bypasses the problem,

* get the model-number and serial-number from the label on the disk-drive, and access Samsung's web-site, to check the warranty-status of your specific drive. If the warranty still is valid, then exercise the warranty to get a replacement.

* if the disk-drive is out-of-warranty, purchase a new, compatible, disk-drive, and connect it into the case, to "reconstitute" your external device.

* if the data on your disk-drive is "important", search online for professional "data recovery" services. For a large fee, they can repair a "dead" disk-drive, just long-enough to copy all your files, and give you the copy.