We have a single kitchen sink with a garbage disposal. Recently the disposal has been "spitting up" water after it runs. We've tried ice cubes, baking soda and vinegar, that has not fixed it. We figured it was a clogged line, I did run some potato skins through previously and maybe didn't run enough water through. So we undid the connections to the disposal and checked the line by pouring water into it, and it seemed to be backed up. After a round of Drano, and using the pipe snake (and checking the fittings to the disposal, no clogs there) water ran through the pipe, no problem. But once we attached the disposal and tried to put water through, it stopped up again. We're hoping we don't have to replace the entire disposal or call a plumber. Again, the disposal runs and grinds food up, but water won't drain through. Also, there's now a leak, where the plastic tubing that connects the disposal to the main line water is pouring out between the gap, which seems very odd, as water normally flows through that pipe no problem now.
First you will need to fix the leak on the side of the disposal. Remove the tubing that leaks and inspect it to be sure it was put back on correctly. If the leak still is persistent, take the leaky part to your local Home Depot and have them find a replacement. Once you have the leak fixed.... First make absolute sure that nothing is inside the disposal blocking the water from draining. If it is all clear then try this... Try a BRAND NEW toilet plunger. Fill the disposal side with water, have someone look under the sink with a flashlight while you plunge the water down. You will usually see water come out of one of the pipes where the blockage is as pressure will make it leak. Where you see the leak is usually going to be where the blockage is. If you see no leak and the water goes down, then it is fixed. This is not very high tech but it seems you have tried all other methods. Give it a try and let us know the results.