(Full disclosure: Bob at Bainbridge Computer Services showed me this trick a few years back.)
Sometimes a dead or dying hard drive can be resurrected long enough to rescue important files, or even pull a full clone.
Drives sometimes fail in a heat-related way. Freezing and then quickly pulling off important data works in a surprisingly high percentage of cases.
I wrap a drive in plastic to prevent condensation (an anti-stat bag is preferred) and freeze it for 2 or 3 hours. Then pull it out of the freezer and quickly attach to a computer. If necessary, re-install it in the original host machine, but it’s better to connect via an external USB to IDE/SATA adapter so it can be kept cold longer. Another approach is to connect to a desktop machine with the case open so the cables can be brought outside the machine.
If using an external adapter or cables to the outside, with the drive still wrapped in plastic, sandwich it between two freezer gel-packs (or bags of frozen peas) and wrap the whole mess in a towel.
If you are lucky, the drive will return to life long enough to copy the important stuff. In the best case, you may be able to clone the drive and avoid a long re-install process.
Here’s an example of an external USB to IDE/SATA adapter. Most of them are USB 2.0 just now. Since speed is of the essence, USB 3 or a direct IDE or SATA/eSATA connection would be better.