[mietl]

OK so I snaked the drain, went in about 20 feet could not get anymore in. put trap back together. Ran water, backs up and it does drain, just very very slowly. Before it would not drain. So now what?

[435Studio]

Can you see how this sink is vented? It could be that the vent is clogged. Are there other sinks that drain slowly as well or is this the only one. To snake the vent you have to get to the roof and snake all the way down. It is possible that this sink is vented with an AAV. If so, when you look under the sink you will see a vertical pipe that extends above the level of the trap. At the top it has a vented cap. If so see if you can remove it by unscrewing. Once you take it off see how the sink drains. If it drains OK you need to replace the AAV. Available as plumbing supply and some box DIY.

[speedball1]

You have snaked the horizontal drain line in the wall. That only takes about 6 feet of snake. The other 14 feet most likely when up the stack but we'll never know.
The fact that you're still clogged tells me the clog's in the drain line below the floor and that can be reached only from the kitchen roof vent. The only other way would be to install a swivel or drop head auger tip (see image) on your snake. If you snake from the roof put out enough snake to reach the base and 18 feet more. Good luck, Tom