I live in an older home (1940) and yesterday my kitchen sink stopped draining. I have removed the P trap and, well everything under the sink, except the disposal, and they are all clear. I ran 25 feet of snake into the wall and found nothing. Now this is what my problem looks like; when I run water into the righthand side of the sink, that has the disposal, it slowley fills, as if the disposal needed to be run, so I did. Then the right side clears but the water comes up the left, when the disposal is then turned off the water levels out in both sides. :confused: If anyone out there has any ideas i would love to hear them.
You have a stoppage elsewhere in the line. Handheld snakes often are hard pressed to do much in stubborn clogs. I'd suggest either renting or purchasing a larger snake or admitting defeat and calling a plumber. I had a clog very similar recently and it required cutting in a cleanout further down the line even with a much more robust snake.
I'd suggest skipping that step and going right to the plumber!