I would use a second computer to build a bootable Ubuntu either with a CD or a USB key. Make sure you select LIVE CD so it won't install anything on your hard drive. It'll let you boot up with another OS and drag your files to a USB drive to save your stuff.
Guide for CD. You can probably google to see how you make Ubuntu boot from USB key.
Use Ubuntu Live CD to Backup Files from Your Dead Windows Computer - How-To Geek