Late to the party, I know, but looking at that picture, you can tell there was some previous homeowner repairs/remodels. The "vent" looks like at one time went to the roof judging by the hole cut in the floor above it, but has since been done away with. It could even still be open at the top, I would look at that. If you haven't had issues before, then you were venting from somewhere, but it's now clogged. Had the same issue in my house. First moved in everything worked great, but after several showers, brushing teeth, hands, etc. a day compared to it sitting 2 years. When the sink refused to drain any water, something was up. Come to find that section of piping that included the vent, was rusted/clogged up to the point of no return.