Installing Mavericks but disk damaged, no recovery or safe modes
So I have a 2009 Mac book. I downloaded OS X Mavericks successfully this afternoon. But when I try to install it, it tells me: "The OS X upgrade couldn't be started because disk is damaged and can't be repaired. After your computer restarts, back up your data, erase your disk, and try installing again. Click restart to restart your computer and try installing again." Okay, fine, but annoying. So I hit restart and end up at this exact same error message. And when I open disk utility, the repair button is greyed out. When I try and open in recovery mode (holding down command - r) it just takes me back to the OS X installer and the error message. When I try to restart in safe mode, my entire computer just shuts off.
When am I supposed to do now? Luckily I backed up my computer last night. But I'm a grad student and a teacher. I need my computer to work. Help?