Go meet with your professor in person, and tell him that during the night before the final one of your roommates overloaded power circuit/fuse to your room and caused your room to lose power. Then you say since I have a alarm clock and the power went out, it reset and my alarm never went off and I slept through the exam. That is your best bet of trying to retake the final. There is no way it can be disproven, and can easily happen. Going to the Dean with a medical excuse is going to be a disaster. Your best off dealing with the professor as it will be informal and the grading is entirely up to him, you go to someone above him they are going to follow strict university protocol, which will suck for you.
My dad is a professor, so I have heard most of the tricks, and I think this is your best shot. O yea the above situation happend to one of my friends, since then I have set 3 alarms, one clock, and two more on my phone before exams/finals, I suggest you do the same if plan on drinking the night before a final.