I'm surprised that a real plumber went through the drain line in the vanity and didn't remove the toilet.
30 to 40 feet sounds like he hit something outside the house. Odds are that it's a root. Especially since the snake is stuck.
I had a house where something similar happened, but they where able to get it out. The one guy that originally showed up started having trouble, so he called in help. Eventually there where three vans, and three guys there, all working on it together. In the end, they located where the issue was in the front yard, and gave me the option of digging the hole myself, or paying them to dig it.
Once I dug down and found the pipe, it was obvious that a root had worked itself into the joint of my drain pipe. And over the years, it had grown to create an issue that needed to be cut out.
The original drain pipes on that house where clay pipe. Probably the worse type of drain pipe ever invented!!!
Before digging, ask yourself if anybody could of flushed something down there that could be removed by a snake?
My grandson stayed with us over Thanksgiving. He flushed some Wet Wipes down the toilet, but my wife thought she caught him and stopped it from happening. My guess is that he kept doing it. The day he left, our toilet backed up. I stuck a hose down the pipe and turned the water on full blast. It took about five minutes, but the block cleared and everything drained to the septic tank.
Last month I had an elderly lady ask me to fix her toilet. It wouldn't drain and she couldn't use it. She is a widow and lives alone, but has grand kids that visit, and a labradoodle dog. After removing the toilet, I found a large piece of bark in the trap of the toilet. Apparently her dog had brought it in and dropped it in there, and she flushed it without knowing it was in there. Usually I find Hot Wheels, Plastic Army Men, and Popsicle Sticks in there that catch toilet paper and creates the blockage.
If he cannot get the Snake out, have him figure out where it's at, and start digging. Odds are good that you'll have to dig there eventually to deal with the issue, might as well start now.
