Up sh*t creek...

Do you have a clean out "t" outside the house? Would be located where ever the drain pipe exits the building...

There are a couple of spots in the laundry room where we have access. The vent line coming down from the roof has a spot with an access cover. This is where our washing machine drains into the line, but we can get in there. On the other side of the laundry room, is another little access cover. This is where our kitchen faucets drain out. Our house is an old postwar prefab that my grandfather had built in the late 40s. There is no outside main line clean out, unfortunately.

I'm almost thinking that we actually have a clogged vent, because our lines do drain. They just drain REALLY slow, and while they are draining they back up a little. We don't have standing water anywhere at the moment. But here's my thinking: If the main vent line is blocked, there's nowhere for the air that is displaced to go, so it shoves the waste back through the pipes until things slowly drain out themselves from the other end. Does that make any sense?