Darko,
It's unlikely the red blade control rod broke before the accident. If it did, the blade would be at a different pitch angle than the others resulting in different coning and assymetric lateral loads. You almost certainly would have noticed a large change in the low frequency (1 per rev) vibrations.
It does sound like you lost power either from governor going to ground idle, clutch problem, etc. The start behaviour and the students loss of altitude are interesting, definitely tell the investigators about that part.
The good thing to remember is that if the power loss was the cause, you did what you had to. Close to the ground you have to pull in all the collective you can. From one meter, the loss of rotor speed is very noticeable and would be much worse from higher up.
Good work in saving yourself and your student!!
Matthew.