First of all, we need as much information as you can give us about your desktop, and your external HDD (make, model#, size, Sata II or III, how connected to your desktop - USB, eSATA, Firewire). Also has the extenal HDD been working properly until this occurred? Anything specific happen just before this problem - power outage, switching the ext drive to a different computer, updates, new installation?
Also go to Disk Management and in the lower graphical area, please list what it says.There are probably 2 rows, the first with data about your internal HDD, like Disk 0, Basic, size, Online; and over to the right under the dark blue band data about the Partitiohs (Volumes) like VolumeName, DriveLetter, size, NTFS, Healthy(primary, system)
In the second row there is similar data about the external drive. Please list all the information there. Importantly does it list a VolumeName and DriveLetter?
That way we can figure out exactly how to get going again.