If the only copy of important data is on that external then perhaps you have selected an appropriate name here.
You should always maintain at least two copies of any data you wish to retain.
USB external hard drives consist of TWO components. First is the exclosure, which is a device that should appear in Device manager. The second is the drive itself, which should appear in Disk Management.
If the enclosure is not showing in Device manager under USB devices then the drive will not show up either.
Follow the link above as a first step to resolve your problem.
One suggestion is to verify the USB port/s you are using are actually working. Test with other USB hardware.