Our kitchen sink would not drain after using the garbage disposal to grind potato & carrot peels. We assumed it was clogged. My husband tried the plunger, took off the trap and cleaned it, used a 25 ft snake from the pipe under the sink through the trap in the basement, took off the trap in the basement and snaked it from the basement up to the sink. At each step he felt like the pipes were clean. Water poured through when each of the traps were off, but when each was reconnected and we again ran the water, the sink filled up and wouldn't drain! Could this problem have anything to do with the vent pipe?

All the other sinks & toilets in the house work fine, so we don't believe it has to do with the main street pipes. Any ideas?

If your vent pipe is clogged you will get problems but more gurgling and burping , not a total drain stoppage like you describe. First off plunging doesn't work on a sink drain that has a garbage disposal or another sink next to it so save yourself the effort. I have a question or two. You said the trap under the sink which makes sense to me, but you then refer to another trap in the basement?? A sink drain line has but one trap, please tell us more or post a picture, thanks.