Roter ruter type snake stuck in 3" ci, wc drain. It has been there for some time. Any hints as to how to remove?

When that happens to me I Put the motor in reverse and pull back hard. If the cable breaks I use a retrieval tip to bring it back. Good luck, Tom

This is not an answer to your problem but sometimes it helps to see what is going on. Technology is great.. Here is a link to a small USB camera which hooks to your lap top and might help you to see what has happened. It comes with a 50 cord. Of course I don't know how far down the drain the broken snake is. Taped to a drain snake and pushed down the drain manually would let you see what is going on and might help in retrieving the broken snake.
I have one, though not with the 50 cable, and they work surprisingly well. For $45 it is well worth the money.

http://www.amazon.com/Waterproof-Endoscope-Borescope-Inspection-Camera/dp/B00E5MBOD6/ref=pd_sim_sbs_indust_1?ie=UTF8&refRID=1ZTK694C92N1Z1DWFBTW