What is displayed in the LR Grid view and zoomed out, IE standard zoom setting (Full image), are Preview images stored in the LR Previews folders. They are not the same as your Real images.
The Backup feature in LR if for the actual LR Catalog files and nothing else. If you didn't back up your images to some other drive I am sorry to say they are gone.
But there might be some hope. It has been my experience that 99% of the time when an external drive fails the actual physical drive inside the external enclosure is fine and it is only the enclosures electronics that has failed. So you should take the physical drive out of the original enclosure and put it into another, New and or Known working, enclosure, or get a USB to IDE/SATA adapter that has it own external power supply, and see if you can read the files on that drive.
If that fails there is always Data Recovery services but they are very expensive and they do not guaranty that they will be able to get the Data off the drive.
If you have the previews you can still retrieve the jpegs but not the raw edited files.
Please follow the steps mentioned in the below article..
Thank you for posting on Adobe Forums.