Sorry to say, but if no computers can read the failed HD as a "source" drive, or from Disk Management or BIOS, then you're not likely going to be able to recover any data from a software utility. Save your money. The only possibility may be to send it to a data recover firm, who may be able to rebuild the drive to recover files. But, if the data is the result of damaged platters, then the files you specifically want, may be corrupted and unusable. Expect to pay major $$ nonetheless.
Hard drives are among the most unpredictable parts in terms of reliability in any computer, and can fail without any advance warning. They can also run perfectly day in and out for many years.
You may just have to learn from the experience, and setup "automated" backups in the future, so no ongoing intervention necessary on your part. Both system image restore and ongoing file backups. If using a laptop, consider using a wireless network HD solution.
My experience has been that those who rely on manually backing up, tend not to keep those backups updated, even though they have both an external HD setup and software installed.
I've setup my computers to automatically backup personal files, photos, and music a minimum of twice daily. I also have a full system image restore for a clean install, and an image backup of my current installation on a separate USB HD. Has worked flawlessly using freeware or open source backup software. Don't even have to think about it?
