Mine's broken too...
I'm having the same problem, except that it's TWO hinges that are broken, not one. Was lying down on my bed reading a document when the screen was accidently knocked flat down causing a heart-breaking cracking sound.
The LCD is fine but it has no support now. The screen can't stand on its own and will flop down. Bummer!
Anyway, I'm going to the nearest Apple support center tomorrow to have it looked at. Hopefully, it's just the hinges that I have to replace. Will let you know how much it costs tomorrow.
cheers!