Is anything else backing up? toilet, tub, etc. I take it this drain runs into the main line under the floor and not through the stack. What are your DWV lines made of, I would assume cast in the floor and possibly copper throughout. Your under floor could have collapsed or let in some tree roots.
Pics or a diagrm would really help, I'd hate to advise you to do something that will make a mess downline or bust something.
If it's just a single line running into the main line and not the stack you could try pushing the blockage through with water pressure. You can get an adapter that goes on the end of your hose and inflates to plug the line and builds up pressure in the line. Could make a big mess though if your blockage is upline from another drain.
A plumber won't be that expensive if they just need to snake that one line, you can't be too far off. You might try a rental store for a bigger snake, probably the safest bet if you don't know the integrity of your lines. If they are ABS though you would be pretty safe with using water pressure.
something like this;
http://www.amazon.com/Cobra-Products.../dp/B000KKRQUM
