A solution I've suggested elsewhere on these forums that's worked for me. If you have a USB stick/USB external HDD and another computer you have access to, use the other computer to download Knoppix (a free CD-bootable Linux GUI OS) and burn it to CD. Then boot your broken computer from the CD. Once in Knoppix, mount the hard drive (right click on the HDD icon on the desktop, click "mount") and you'll be able to browse it as you would in Windows.
Then plug in your USB stick (Knoppix supports hot swapping), mount that in the same way and change writing permissions to "write only" (in the same right-click menu as where you mounted it.) Then you can simply drag and drop files from your hard drive to your USB stick as you'd be able to in Windows. Once you've done that and you're satisfied you don't have anything else you don't mind losing, you can go ahead and reformat your hard drive using the supplied recovery CD.
If Knoppix won't detect the hard disk this way or you can't see or move any of the files on it, then you can probably assume the hard disk is knackered and you need a new one. These things do happen unfortunately - I've had to replace two hard drives in computers at home in the last few years simply due to wearing out.
If you need any further help using this method I'll be happy to help.