If you type diskmgmt.msc into the search bar in the start menu and press enter - can you see the drive in that menu?
There are 2 parts to a usb drive - the controller and the actual 'storage area'. The controller is what manages the interface between the drive and the computer, and is what makes it show on your desktop taskbar. My Computer looks for the storage area and will not show the drive if it can only find the controller. It could be that the storage device is dead but the controller is fine, which would cause the symptoms you are describing.