If you really need something out of it, and now, here's a couple of tricks you can try:
1) Put the HDD in the freezer (yep) for 30 minutes
2) While waiting, bring a fast-booting computer with absolutely minimum on-boot programs loading
3) Take the HDD out of the freezer and connect it to the computer mentioned above (while it's off), and boot it
4) Now, try to think of all you need in priority order
5) As soon as you can, access the HDD from the freezer and start copying to a working HDD on the computer
If you can't get all, try to repeat the trick once more.
And here in the northern parts, you can try a similar thing in the winter, but with an open window + table fan instead, allowing for more time to copy:
1) Connect the HDD to a computer, and leave the case side open
2) Take the HDD as far out from the computer as you can, and take the entire thing next to a window
3) Now, setup the table fan to blow cold air from outside - preferrably -20C or colder, and try to pick a day when the humidity is 0 % - directly at the HDD
4) Let the fan blow at the HDD for 15 minutes or so, until it is very cold to the touch
5) While waiting, make the priority list
6) Boot the computer and leave the table fan still on
7) Now, copy all stuff to a working HDD on the computer until the system freezes (figuratively
)
The table fan method allows for a bit more time to copy stuff (about 25 minutes, instead of 10 minutes, from my experience) than the freezer trick, but you can only do it in the winter, and on the second repeat you can't copy quite as long. In total, it's still well over twice the time than with the freezer trick (30-35 min instead of 20 minutes).
Good luck!