The easiest way to backup stuff in this situation is to get an external hard drive and connect it to the PC, somehow acquire a copy of a Linux Live disc of a distribution that supports NTFS formatted partitions and boot off the disc. You will be in a Linux operating system that runs 100% in RAM and does not touch the hard drive at all allowing you access to functionality that you otherwise couldn't access like a web browser, hard disk recovery software etc. Simply copy stuff from the broken HDD to the external.
Edited by franpa, 03 October 2011 - 08:54 AM.