That you have a seriously clogged drain is to state the obvious. By your description, it would appear the clog is major and fairly deep into the drain system. What is needed is a plumber with a "real" snake that is not only long enough but with a large enough cutting end to clear the clog. This is not a DIY project. The industrial sized auger requires skill to operate and in the hands of a novice can be literally deadly. Most of the pros advise avoiding the companies with "Rooter" in their name.