I know first hand that hard drive failure can come in many forms and can be very difficult (and expensive) to handle.
About a year ago our office server had a hard drive fail while we were in the process of installing updates. At the time, it was running Fedora linux, so we were afraid it was just a software corruption. However, after investigating into BIOS I realized that the drive would not show up no matter which port it was connected to.
Unfortunately, our system was also set up in a software RAID 10 setup which didn't work properly as it should have and did not allow the system to recover at all. Our only option was to send all 6 of the 500 GB hard drives off to be examined and determine if they could have data copied off. Again, I had checked each of the drives individually and was able to see areas of data used on all the drives except the physically fried hard drive. However, the data was not "in tact" because of the RAID and the missing hard drive that had failed.
So we contacted Data Recovery Services online. They are one of the foremost data specialists in the U.S. and my uncle, who has done similar work for NASA, Boeing, and the US Treasury Department, recommended their service for this.
We filled out the information and shipped the drives in next-day express mail. The following day their tech called and said they would be able to recover all files and would even be able to put the data onto a new drive for us. They sent us a quote, which was over $1,500.00 because of being so many hard drives in a complex Linux RAID, but in the end since all we needed was about a DVD worth of files backed up, they dropped the price to less than $1,000.00. Not only that but to make the whole situation better they went ahead and backed up and sent back all the data from the drives, not just the small list of folders that we needed.
I would highly recommend them again if, unfortunately, similar situations occur for others I know. They are very easy to contact and very quick, though you have to understand their services aren't cheap. Still, for a single hard drive (depending upon the actual amount of data) I imagine it would be between $500 and $800.