I would shut down the computer first. I'd connect a mouse to one of those USB ports that were used that 'failed'.
Start up the computer and when Mousing becomes available (at the log-in screen), wait a minute or so for 'recognition'. I want to see if that USB port is 'dead'.
USB ports can suffer 'death' by static discharge - especially aggravated by Connects and Disconnects when electrical current is running thru them. The formal "now you can disconnect USB device" process supposedly eliminates this, but your comments about Plugging Unplugging make me wonder if the USB ports are dead.
If I had USB memory sticks that CERTAINLY work (Guaranteed, absolutely positively tested on another computer), I might also test out those other USB ports to ensure they're all functioning.
I would conduct all of these tests with 'hard' Shutdowns, too. I'd shutdown Windows, power down the computer and plug-unplug my testing USB devices each time with the Power off.
Very time-consuming, yes, but it can be the least hazardous and most certain way to test a USB's connectivity.
Once I knew those ports worked, THEN I could start casting doubt about the External Drive's life. External drives generally have 3 types of failure - (1) the USB plug/cable has died, (2) the power supply has died, or (3) the hard drive has died.
The first two 'deaths' can still leave you with a working hard-drive at least, and it can be extracted from the external case and re-connected to recover the files.
The last one, well...