yeah sounds like the main drainpipe is clogged.That big a pipe a snake is useless most times. I bought a tool at the improvement center that attached to the garden hose,and pulled the toilet up, shoved this tool in the pipe,and turned on the water. It swells to the size of the pipe and won't move,and uses the water pressure to unplug the drain. Worked pretty well. Cost like $20.
Don't remember what it's called.I'm sure if you describe it to someone at the improvement center they'll know.
Oh better do this at the basement stool
Good Luck