How do I save files on Macbook with crashed OS?

I have a Macbook that the OS has crashed (I am not 100% sure if the Hard Drive is dead, but I would like to save the files before anything else). When I boot up, the screen just remains grey and there is a spinner that stays on forever. I thought that if I got a thunderbolt cable and connected that Macbook to my other Macbook Pro, I could boot the crashed drive Macbook into Target mode and then get access to the files. That doesn't seem to be working and now I am re-reading the instructions it seems that the target computer needs to be bootable (i.e. into OS X, which mine is not). I'm not familiar with how to take this unibody MacBook Pro apart. So how do I get access to those files, before I reinstall the OS?