Black Screen But Can See My Cursor

So every time I boot up my computer I am getting a black screen but my cursor is responsive. I tried rebooting in recovery mode but could not reinstall my OS because of Apple being unable to "verify" my computer. My macbook is a 2010 but I was just as the Genius Bar over Christmas to have my computer checked out and they said everything is running great. Any ideas? Solutions?

I live 3 hours away from the closest apple store so anything anyone can recommend would be helpful.