I am not a professional plumber.
I have no idea how much it would cost to dig up and remove that pipe. I can't imagine that it would be less than a few hundred dollars.
Having said that, perhaps you could contact a drain inspection company. You know, the one with the camera.
Have them run the camera down to see what the cable is hung up on.
Like people here have said, maybe it's a busted drain pipe or tree roots or a ball of gold coins. Who knows.
By running the tv camera down your drain you'll know. The operator should be good enough not to get his camera stuck on whatever is hanging up the snake.