OK, now try this. It may or may not fix the problem but no harm will be done.
Download drivecleanup.zip v0.8.1 from Drive Tools for Windows
. Unzip it and you will have two folders containing DriveCleanup.exe, one for 32bit and another for 64bit. Copy the one appropriate for your system into C > Windows > System32. Unplug all external USB devices except your USB Keyboard/ mouse.
Open an elevated command prompt, type drivecleanup.exe and press enter.
This will clean up all old USB drivers and you will be starting with a clean slate.
Reboot your system.
Plug in your USB devices. Appropriate drivers will be installed for each USB device.
Safe remove all your USB devices.
Shut down your PC.
Plug in your Verbatim External drive, boot your PC and now check whether it comes on with Windows start.
If my reasoning is correct, this should fix the problem.
My reasoning: Windows was loading a wrong driver on startup. That came about because it was connected when Windows was installed and it continues to load the same wrong driver on startup. This procedure removes the wrong driver from its store and you have put in only the right drivers. ( I periodically flush the system with drivecleanup.exe and when I do, I reassign the correct drive letter to my external backup drive so that backups go to the right drive.)