Q: My Seagate external hard drive does not show up.

are you running any seagate software? if so uninstall it.

disconnect all external devices and boot into safe mode

Try safe mode if your Mac doesn't finish starting up - Apple Support

then connect the device

if it does not show go to Disk Utility and see if it appears

if not try another port on the computer or another cable or another computer

if all those fail the drive could be going and you should contact Seagate and see if it's in warranty to be replaced.

I had similar problem, the seagate hard drive showed up in the disk utility but could not get it to connect,

I opened system preference to find the Paragon NTFS file for Mac OS X and selected the option to turn the driver off for Mac OS X, the Seagate hard drive showed straight away.

Seagate has a knowledgebase article and walkthrough on how to solve his issue. Hope it helps!