I don't have much good news for you. It is likely the drain pipe is galvanized steel which is highly corroded, probably nearly closed. There is only one real cure, a very costly replacement of the drain lines. You might get some improvement with a professional augering, but that could backfire if the pipes are really badly rusted as the auger could open the pipes. I will tell you one thing not to do. Do not use chemical drain openers. The not only don't work on corroded drains, they could eat right through the pipes.