How to backup Mac without login???

My iMac has a very weird problem, it usually booting with a long gray bar and take very long time, and even sometime it suddenly shuts down while booting. And now it shuts down every time i turn it on. I did try Lion Recovery to repair Macintosh HD, but it can't repair, there is an alert that tell me I have to reinstall Mac OS, but before that, I have to format Macintosh HD, and it will erase all of my data. And OMG, I forgot to backup my iMac, what can I do, please help me?!!!