One thing to try first, and it is just "guesswork" and a long shot.
Get an antistatic bag (you do have some lying around, don't you), put stick in that, squeeze as much air out as possible, seal, stick in freezer for 20 mins.
That MIGHT mean a bad solder joint contracts enough, with everything else, to "make" the contact again for enough time for you to grab the data off with some decent recovery software (a list is in this forum). It worked with me ONCE with a memory card for a camera that decided to "give up the ghost", but I guess you got nothing to lose now.