Judging from your problem, your only choice is to take your external HDD to a hard drive recovery specialist. If your device still has the warranty, then don't hesitate to contact the services. You cannot fix this issue alone since you have to open the drive and thus leading to the void of your warranty (and you might even break badly your device if you don't do the steps carefully!). Not forget this must be done in a dust-free environment, so ye...

The good thing is, you'll learn (hopefully) your lesson that backups are always worth for your valuable data in two devices at the same time. Don't treat these as reliable storage because they aren't.