Your drain is clogged, and you have discovered that DIY snakes are usually worthless. Likely your efforts have either not reached the clog or have just pushed it farther down the pipe. What you have to do is call a professional plumber with profession equipment. Snakes that would be big enough for the job are seldom available for DIY and even if you found one they are extremely dangerous in the hands of a DIY. Dangerous like will take a hand or arm off. You did get a very good toilet.