After trying that backup...
If you can't copy the files, you can,if necessary, use "dd", skipping eventual bad blocks, as explained here.
http://www.linuxquestions.org/questi...-drive-764487/
After you have secured the files, you might use Google to find the HDD makers utility program, HUTIL, SeaTools, etc., and run it to check the HDD. If there is no utility, try SMART. Check your BIOS and HDD to see if it is activated.
Unless any future content isn't of any importance, the HDD rule is, when in doubt, throw it out.