USB hard drive not recognized by Mac and by PC

Does the external drive work when connected to some _other_ computer? (Friend? Office? Home?)

It could be a failure either in the "hardware" inside the external-case (the USB adapter & interface)
or in the disk-drive "inside" the external-case.

So, a qualified technician can open the external drive, remove the disk-drive, and connect it directly to a computer, to see if the files can be "directly" read from the disk-drive.

If not, then you should search online for a "data recovery" service -- they are expensive, but they physically repair a damaged disk-drive, just long-enough to copy your data to another disk-drive.