How to backup from recovery mode.

I have a 2009 Macbook pro which will not start up. One day I turned it on, but will not get past the Apple loading page. Since then, I have tried everything to solve this except formatting and reinstalling. Before I do this, I would like to back up the contents of the hard drive (they havn't been backed up before) to a time capsule.

How can I go about doing this? I can open disk utility in recovery mode, but the time capsule doesn't appear (when plugged in with both usb and ethernet). Why isnt time capsule appearning in disk utility and how can I backup my HD?