I can't help you with an answer but I have a similar draining issue in my kitchen sink. Nothing else in the house is backing up - just kitchen sink. Drain is right above unfinished basement so I unhooked the trap (P-Pipe) in the basement, cleaned that out with not much coming out of there. Then I ran 15 feet of snake into the PVC drain pipe and felt no obstructions. Still won't drain so .... I too am stumped. I snaked past where another drain is joined to this drain and nothing else is backing up. Doesn't make sense to me.