Our sink has been clogged for a couple days and nothing is helping. Plumbing

Before I get started, I have almost no idea what i'm talking about, so if I sound stupid or don't know the name of something, sorry.

A couple days ago my mom was cleaning out the refrigerator and I'm assuming she just put too much food down the garbage disposal. The sink will almost completely not drain and we've ran out of ideas. I tried using a plunger but that didn't help, my uncle came over and we tried using a snake (I'm assuming that's what it's called). Then we used that snake on the roof on the exhaust pipe thing that runs to the sewer, twice. None of these things helped.

From there we poured some extra strength drain opener (sulfuric acid based). After it sat for a little and "drained" it (not sure if that's the right word), it was still clogged. My uncle's assumption is that there's something deep in there that just wont come unclogged, kind of obvious, but yeah. We're officially out of ideas, does anyone have any suggestions? Also here's a picture of the pipping under the sink because I think my post requires it

Submitted December 21, 2014 at 10:26PM by Semajj http://ift.tt/1AU1Gf3 Plumbing