My bathroom sink has been plugged for a few weeks now, and I've been trying everything. I'd rather not hire a professional, but it may come to that.

The sink is pretty much completely plugged, and only has a very, very slow drain. The toilet and the shower drain fine, though there is a bit of a gurgle when the toilet is flushed. I've tried plunging the sink, but when I do, nothing goes down and all I get is some black, charcoal-like gunk in the water that is pulled up by the plunger. I've pulled the trap and run a snake through the drain, and I can make it about 10 feet or so before it won't go any further and I never get anything back with the snake.

From what I can tell, the drain from the sink runs into the vent stack for the toilet. The sink sits about 3 feet from the toilet. The toilet drain and the vent is all cast iron, and the sink drain looks like it is cast iron as well once it enters the wall.

Any suggestions on this? Could there be a blockage in the vent stack that would cause this kind of issue? Would using a hose to blast out the blockage from the sink side work? Or is there something else I should try first?