I have a couple of questions for you in order to help me answer your question.
1. Do you have a garbage disposal in the sink?
2. How much snake did you run? (how many feet)
3. Do you have problems with any other drain in the house?
Thanks for your reply. I'm eager to help you sort out your problem.
What is probably happening is when you snaked the vent you snaked into another branch of the same vent. Many times a vent stack sticking through the roof will have more than one drain that it vents. So snaking and adding drain cleaner will not clean the vent that you need it to.
The only way to be sure that you are snaking the right vent is to have someone listen for the snake in the pipes at the sink in question. This also applies to snaking from the bottom up.
If the installer did not use the proper fittings it will be almost impossible to get the snake to go into the line you want it to.(see drawing) If this is the case the only solution is to knock out enough of the wall to get to the bad connection and then clean it out and preferably put in the correct fitting.
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Best regards; The Home Smithy
Ok Dave I think its time to put a little pressure on this problem.
What I would like you to do is use some pressurised air and see if that will make the problem flow any better. All you need is a source of compressed air. A carpenters compressor will work fine if you have access to one. If you dont then you can get a small compressed air tank, and an air nozzle, at your local hardware store for about $25.00. Get an old tee shirt and get it wet. twirl it up into a semi tight twist and wrap it around the air hose nozzle so that you can pack it around the nozzle in the sinks drain basket. If it is a two hole sink use another tee shirt to plug the other hole. You will need more than two hands to do this. Before you set this up be sure that all fittings are tight.
Give the air tank nozzle a squeeze. If it seems to flow freely without wanting to come out around the rag(s) keep going. Do this till the air tank either runs out or the air begins to back up. With any kind of luck it will start to back up and then release, blowing whatever is in your line out.
Now this may sound like it will never work because you have snaked all the lines out. But somewhere there is a line that has not been snaked.
Now that you have gone through one tank of air, you will need another. But this time go up on the roof and put a cap on the vent stack. One of those that have a water hose clamp with it. Do the pressure test again. If nothing happens you will need to find a way to close off each line in succession and pressurise the others. They have rubber balls made to do the burried lines with, that have a recovery chain, and fill hose attached to them. You should be able to rent one at the local rental yard.
Use your ears too. Listen to what the air sounds like and where it may be going. If you have a line that doesnt sound like any air is going through it that may be the problem line.
I know this sounds like a lot of work. But believe me I have been there and done that more than once. Only diffence is that I now own all the right doohickeys to do it with.
Good luck and if you have any more questions don't hesitate to post them.