Here's my 2 cents: Attack the problem on different levels. Sure, you want her to eat again, but more importantly, you want her happy. Its unlikely she's going to blurt out what it is that propelled her along this path (-- a fellow she had a crush on thought she was fat, perhaps? -- sometimes its not that simple) -- but what IS important is to make her happy. Make her laugh. Really, really laugh. Happiness and laughter always dispel self-destructive behavior any time. Don't tell her to "snap out of it" (she'll probably eat less just to spite you.) Try to remember a time when she was really happy. Did you ever go on walks together? Was there a favorite movie that she just loved as a girl-- something she may not have seen in years -- anything you can think of that will trigger happier memories of younger (and more innocent) days. Were there projects that she helped out when younger? Redecorating? Painting? You can pretend to solicit her help in a new project now that focuses her mind on the task at hand. Maybe redecorate her old bedroom? The real key in loving someone is to make them believe that they have something worth contributing. And with your daughter, that won't be hard.
For what ever reason, her self-esteme has taking a beating. But love and patience can repair the damage.