The external storage device has several major components:

* USB cable

* external power-supply

* disk-drive inside the enclosure

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

Try a different USB cable.
Try a different USB port on your computer.
Try a USB port on a different computer.

Take a multi-meter, and measure the output voltage/amperage of the power-supply,
and compare with the specifications on the label of the power-supply.

Open the enclosure, and remove the disk-drive, and attach it as a "slave" drive in a desktop computer, to see if bypassing the USB-to-disk-drive adapter bypasses the problem.

Look at the label on the disk-drive, for manufacturer, product-number, serial-number, and manufacture date. Access the manufacturer's web-site, and use "check warranty status" to see if the warranty still is valid. If so, the drive can be replaced, at minimal cost to you.

Buy a new, compatible, disk-drive, and install it in the enclosure, to "revive" your external storage device.

Search online for a professional "data recovery service". For a significant fee, they can repair your disk-drive, just long-enough to copy your files to a new disk-drive.