Up sh*t creek...

I mean that more literally than figuratively. The main sewer line in our house is clogged. No matter what faucet is run, water backs up through the floor drain into the laundry room. Same if we just flush the toilet. It doesn't just stand, though. It still drains slowly. There's also a lot of air that bubbles out through the floor drain when we flush the toilet. We pulled the toilet tonight because we needed to replace the wax ring anyway. We snaked the toilet line while it was up. Put all 20' of our handheld snake in, and didn't hit a thing. Tomorrow we are going to see if we can pull the cover off the floor drain and snake it from there. Hopefully we strike oil in the process, because if we can't clear it ourselves, that's the only way we'll be able to afford a plumber. Any advice? Our house doesn't have an outside clean out like newer houses do. We just have the floor drain and the pipe where our washing machine drains in the laundry room for access. And the house sits on an slab. Thanks in advance for any pointers you can offer.