Sadly, there is rarely anything you can fix on your own with external drives.Replacing the drive is the cheaper solution!
But! Clearly the issue is not the physical drive its the data it holds. Your only choice is to ship your drive out to a data recovery service. Unlike you they have the needed tools & parts to replace to get the drive going long enough to pull the data off. Yes, its expensive! There isn’t anything you can do without the needed clean room.
Take a look at this vid: [https://www.youtube.com/watch?v=R5-7WZfbZuQ|Hard Drive Data Recovery Service - DriveSavers]