Evidence of solid waste means there's a clog somewhere. Without knowing how your house is plumbed, one branch could easily be clogged and the others working quite fine. FWIW, a toilet will flush with no vent at all, so that isn't the issue. Pulling the toilet can give you a closer path through that drain line. But, the typical homeowner's snake is not designed to scour the larger lines and often will just poke a hole, that will quickly plug back up. 40', depending on the house, could easily be out into the yard on the way to the main sewer line.