Data recovery after OS failure using different computer

Noticing that the hard drive doesn't sound somewhat weirdly and that the machine does detect the disk and doesn't report on any problems with it means that the hard drive is luckily intact. Unbootable operating system in this case doesn't mean that the data are lost forever. Using proper software and following simple recommendations you are in with excellent chances to recover lost files.
If it's technically possible you should carefully remove the drive from your computer and connect it to another computer by means specified in
How to: Connect IDE/SATA drive to a recovery PC article.
After drive connection is successfully done it's strongly recommended to create an image of the drive using disk imaging software. Disk imaging is only a precaution that will allow recovery software to work in a safer virtual environment. And yet, recovery procedure can be accomplished from the hard drive itself. For recovery from a hard drive or its image SysDev Laboratories advise applying UFS Explorer software. These application combine a set of all tools necessary for recovery from a failed operating system. The utilities are designed in a user-friendly wizard manner that makes them simple in application. If the examination produces good results meaning the system is intact you can copy the data from your hard drive to an external storage. For corrupted file system you should accomplish actions specified in software manual. Damaged data can also be just copied from the operating system to an external storage for further reference.
Simply install the software to recovery computer and start getting your data back.