I guess there must be some kind of blockage in there, but for the life of me I can't find it. I can't get the engine running at all at this point, aside from some brief sputtering sometimes. I haven't been spraying in carb spray, just "Starting fluid", though maybe they're similar?
Do you think it's worth buying a new carbeurator? This is a replacement part (https://www.amazon.com/Zeaauto-Lawnmower-Carburetor-Stratton-799866/dp/B0157T94R8/ref=sr_1_3?s=lawn-garden&ie=UTF8&qid=1496242350&sr=1-3&keywords=briggs+and+stratton+799866)