If it were actually inexplicable, someone would have started a business to do it for much less. The fact that no one has (or has, but failed to stay in business) indicates that it's probably an expensive and high risk business.

What is the problem exactly? This makes a big difference in how you go about getting data off of it.

Does it not spin up? Maybe this will help: http://web.archive.org/web/20080207080550/http://www.deadhar...

Does it spin up but have lots of errors? Try mounting read only from a Linux live CD and use dd with the noerror option (this tells it to keep going even if there are errors) to mirror the contents to a new hard disk (same size or larger). I've used this technique many times over the years, and usually gotten most of the data restored.

Freezing is a method of nearly last resort, IMHO. After freezing comes "take the platters out and put them in a whole new, but otherwise identical, drive". This one is entirely last resort (and assumes you don't plan to use one of those expensive services, since this will be the last thing you ever do with this drive), and assumes your data is worth the cost of a hard disk to be thrown away at the end. I don't actually know if you can even get the platters out of modern disks, but I've done it in the olden days...maybe 10 years ago...and was able to recover some data, but nowhere near most. The disk gets eaten up with errors within a few hours of spinning up after using this technique.

The expensive services presumably have clean room conditions for performing the last technique without the resulting destruction of the drive. They also probably have variable speed enclosures to allow slow reads of data (I'm guessing, but if I were building tools to operate such a business, that's the kind of thing I would be working on).

And, of course, the best way to fix a broken hard disk is to replace it and restore from recent backups.