I have the same problem except the bath is on the second floor. The sink runs for a few minutes then backs up... takes about an hour to drain a couple cups of water. The toilet and tub are just fine, everything on the main floor is fine. I have tried to snake the drain, but came up with nothing execept a black sludge. I tried an enzymatic cleaner and it helped a little but not much.
Any ideas would be greatley appreciated.
Thanks
