Flashing Folder with Question Mark, Disk Utility Grayed Out

I was working on my macbook pro when it appeared to freeze, so I manually shut it down by pressing the power button. When I pressed it again to restart the computer, the restart "chime" sounded, and a flashing folder with a question mark appeared shortly after. The folder flashes for a few minutes, and the macbook turns off again. After consulting the internet, I restarted while holding command+r, and the computer told me to reconnect to the internet, select a language, and so on. When I reached the menu giving me choices for how to recover my information, I discovered that there were apparently no time machine backups recognized and when I tried to use the "first aid" option in Disk Utility, all of the action buttons are grayed out when I select the drives (I'm running OS X Mavericks) at the left, including the "Verify" option at the top. Is there anything I can do? I really would rather not restore a new version of OS X to preserve my information.