Sulfuric acid took care of the the hair clog from my wife and daughter a couple weeks ago. Took about an hour to do it's thing. Those hand powered snakes are pretty much useless for big clogs. Not enough power to grab the clog, that is if you can get it down the pipe far enough to it. And you will spend an arm and a leg for a decent plumbing snake that you can hook a drill to it to get some power.
If you can't get it to open with chemicals or a hand powered snake. You're better off calling a plumber. A decent snake that is not hand powered will cost a few hundred bucks from hoe's depot