Hi there,
Try plugging the external drive into your laptop and turn the ext drive on, before turning the laptop on. That way when the laptop boots up, it should be recognized.
Also when booted up, go to Computer management, and see what it lists in the bottom graphical section as to the Disk status, and Volume status.
The BIOS detects a drive as "Disk 1" etc., the OS recognizes the Drive by drive letter "G", and Windows Explorer uses the "Volume Name" in the file structure.
List for the group the Disk Status (Basic, Disk 1 or Removable, size Online, or what is there) and the
Volume Status (Volume Name, Drive Letter, size, NTFS or other file structue, and Healthy(Active, Primary Partition, or what is there).
Then someone can better determine if anything is amis.