Wresting files from beyond.

[Bee Happy]

I've neve done a lot of work  in this area before, mostly because I was better prepared than this time...
I'l be as descriptive as I can. The computer I'm on now started its life as a windows 7 unit. it crashed after about 2 months of use (and was my 3rd computer in 3 weeks, a reliable old one finally puttering out, a brand new one barely better than a doorstop, then this one @ #3 with win 7. still not done counting OSs. Then because I had school to deal with and needed an OS right away (instead of time and expense in the shop) so I bought a SATA drive and external drive case - installed linux mint - transferred my files from the crashed HD and away I went.
a few weeks later - the new hard drive slid off the deck (of the laptop being carried elsewhere) and onto the floor -breaking the case open and getting some unnoticed moisture in it as well. - it booted  ok for twenty or thirty minutes, then faded out like a sinking boat.
 - New SATA XHD - this one shock and moisture proof - linux mint again. (82nd times the charm?)
Now the core issue - when I plug the old HD in to the USB with the new drive (also USB) running the OS - the computer recognizes a "file system" of around 250G then the fun starts - I gently try to find my way into the old HD (which the comp eventually advises me is in danger of critical failure) it refuses to mount, open, or display the files. I've almost resigned myself to the files (almost all writing, some pics, a few videos  and in addition pretty much all of my earth shatteringly brilliant classwork) being lost and having to go back to my CD stored versions from almost a year ago without revisions made more recently.   - Unless someone knows a command or linux program I can use to tear the files I KNOW are floating in storage just the tiniest bit past the reach of my outstretched fingers - back to somewhere I can call them mine again.

EDIT: My wife has the same computer still running windows 7 - if I put it on there it  recognizes it as a SATA drive but thinks it's a "printer" or some other USB junk that can't be accessed.