You might want to look at DataResuce http://www.prosofteng.com/products/data_rescue.php
You'll have to decide if your files are worth the investment. There is a free trial that will show you IF there are files that can be rescued, then you have to purchase in order to actually recover them.
Thank you, Mike. I have bookmarked that website for the future.
The external HD inexplicably decided to mount to my Mac after the fifth or so try of me turning it off, unplugging it, and then turning it back on and plugging it back into my Mac (perhaps my swearing at it helped? ) and I used Carbon Copy Cloner to back it up to the new external HD, so my problem has been solved.