I have a Mac OS X EI Capitan Version 10.11.6. Also got a 1.5Tb Seagate External hard drive. The hard drive is about a year old and my mac is only a few months old. The hard drive always work fine, but when I plug it in now, it doesn't mount at all and doesn't even show in Disk Utility? I thought of just re-formatting the hard drive. But I can't format it if it doesn't show in Disk Utility, it also doesn't show when I go to the Terminal. Type in diskutil list, it only shows my Mac hardrive. The hard drive is running, I even replaced the usb cord but still nothing. It doesn't even show up in my Time Michine. I added screenshots. Please can someone help me.
Barring also testing it on another Mac, that sounds like a hard drive logic board failure. Your best bet might be to source a logic board from another identical hard drive, with an IDENTICAL board model identifier (including the revision if any), and swap for yours, then see if it works.