Kitchen sink backing up into pipe vent and spilling out?

When empty my dish water in the sink it flows back up into the straight pipe that i was told is a vent? It is completely ruined the boards under the sink. No other drain in my home is backing up or having issues. I have snaked the drain with a 50 foot snake and put liquid plumber foaming pipe snake in I have used original drano and used vinigar and baking soda. and boiling water. Nothing is working. I can't afford a plumber. What should i do. Also if i HAVE to call a plumber what should it cost?