If the data is truly critical, you need to send it out for recovery, because there's always a risk that the steps you take to attempt to fix the problem will cause further damage. (For example, if you have a failing bearing, running the drive will likely make it worse.) On that note, I'd recommmend searching around in the
Ars Technica "Other Hardware" forum. There are plenty of people there who would be able to advise you about this, and plenty of old posts which ask pretty much the same question. From reading it in the past, it seems that their recommendations often involve companies like OnTrack and DriveSavers. And it won't be cheap to use their service; probably between $400 and $1200.
If you're willing to take a little bit of risk, or suspect that it
isn't a degenerative sort of problem, then by all means, try the other solutions. In Windows, a simple CHKDSK will usually correct simple stuff like a damaged file system—I'm sure there's an equivalent command on the Mac (fsck or something). If the circuit board is visibly damaged (burned components, for example), it's often possible to retrofit an identical board from another drive (voiding the warranty on both).