The indicator light flashes because the hard disk is reading data, and the drive letter you mentioned is not always displayed. This may be because your connecting cable is not plugged in correctly. Generally, there are two plugs at one end and one at the other end of the connecting cable of a hard disk. Check one of the two plugs and don't plug it in.
Or just your computer doesn't have a display. Right-click on My Computer → Manage → Disk Management → There are several boxes below showing your local disk. Just find the unmarked right button and set one.