|What is the status of the external drive when looking in Disk Management?|
You can try a live version of Linux, like Knoppix, which should be able to recover the files.
Or you can try recovery programs which either show you what can be recovered after purchasing or allow limited recovery. Look below.
Get the file about 2/3 of the way down.
Knoppix V5.1.1CD-2007-01-04-EN.iso 94-Jan-2007 00:58 696M
PC Inspector (freeware)
Zero assumption Recovery
The demo is limited
It will only recover 'up to' four folders per run
But you can make multiple runs
IMO the best, but not free
After file recovery you could try to repair the partition with Testdisk. Get it below. Be sure to read the tutorials thoroughly.