Sink/garbage disposal won\’t drain unless the disposal is on

I have a sink with a garbage disposal, and the sink won\'t drain unless the garbage disposal is on. I have run ice cubes in the disposal, taken the plumbing from the disposal to the wall apart, checked all the pipes, and run snake 20\' down the drain pipe.  I still have the same problem.  Can it be the disposal or would the pipe be clogged beyond 20\' (No water is in the drain pipe.)