Broken Disc for Xbox 360?

Okay, so I put in my disc (Left For Dead 2) and it makes the noise where it blows out air (which means it's about to start it up) but then abruptly stops. Then, my xbox has a black screen. I try taking the disc out, but it doesn't even go to the dashboard. So, I have to restart my xbox. Well, after retrying this again and again I finally decided to try it on my Black Ops disk. It worked perfectly. So, I cleaned my disc with alcohol and I ran it under hot water. Nothing worked. Please help me. Is there anything else that I can do? Is my xbox just messed up with that game? Thanks in advance.