As luck would have it, this afternoon, I had to pull two photos off my phone and onto my laptop. I followed my own advice, and lo-and-behold... it didn't work! 
Here's the thing though, I realized the USB cable I was using was not the one that came with the phone. It was essentially a charging only cable that came with a BT headphone. Not all USB cables are created equal. Some are in fact for charging only. Some will support charging, but at slower speeds. Some will provide for charging and for data transfer.
I used the cable that came with my phone and had no problem.
Anyway - the take-away should be to try the following:
1). Reboot the phone. Try again.
2). Make sure you are using the cable that came with the phone.
If you're not sure, you might have to hunt up another cable... one known to work with someone else's phone on their computer.
3). Try using another USB port. Do not use a USB port on the Keyboard or the Monitor.
4). Reboot the computer and try again.
You can also try another person's phone. Or you can try your phone and cable with someone else's computer.
Now then, there is a known problem with USB ports on Windows computers, that then will not recognize ANY devices plugged into them. There is a means to delete the USB hub in Device Manager and reboot the computer to have the computer re-add the USB hub. You can Google that if none of the above worked.
Hope it helps.