Welcome to the forum.
Unfortunately, the Elements Organizer just links to the Asset files. If they are stored on a damaged external HDD, there might not be anything to link to any longer.
Now, with damaged HDD's (both internal and externals, when I could get them to spin-up), I have been able to use several file recovery tools to "restore" the files, to a new, safe location.
I have used Stellar-Phoenix Recovery Suite, and also Recover My Files. With file recovery, not every utility will work perfectly in each situation, and that is why I have two, that I use.
Will that damaged external HDD spin up?
Do you get an OS error message, if it does?
To what degree is your external hard drive damaged?
I do not know what level you are at with regard to computer and Premiere Elements usage.
So, please excuse, the just in case question....when you say damaged external hard drive, are you referring to more than its drive letter changing on you spontaneously?
Is the external hard drive reading anything even if you take Premiere Elements project source media out of the equation? What computer operating system are you using for Premiere Elements and this external hard drive? And how is the external hard drive formatted - NTFS or FAT32?