Yes, what is that definition of Ki that everybody seems to agree upon?

Part of the problem is that we in the western part of the world, have disconnected the original meaning of ki, and have given it a limited meaning that we apply only to the martial arts. This limited version of ki leans too often towards something magical. Some think that some have it and others do not. As there is no solid definition of this limited version of ki and there is no longer a connection with the original way of thinking we unwillingly create our own vague ideas about ki.
The Japanese teachers that I have met don't have any problems with the idea of ki, as it is a common word in the Japanese language. Even without giving it much thought they naturally associate it with a mood, a feeling, a thought, the mind, life (if people do not have ki, they are deceased), etc.
Ki is like spirit with its Latin - Greek history, a word rich in associations, interpretations - a word with a very long philosophical history.
We tend to associate ki as only having to do with the application of a technique. But in Chinese/Japanese philosophy, as has been taught to the samurai for many centuries, ki not only refers to martial skills but ki is the "carrier" of ethics and esthetics. This explains why in Japan even today budo grading is not just given based on being successful in throwing (our Western idea of objective results), but just as much based on ethical behaviour and esthetics.

Without its original context ki has become a rather poor, meager word and it is this limited version of ki that is creating much of the confusions.

In day to day life we already use different words to explain ki to people unfamiliar with the word. In that sense we do not really need the word ki.
Personally I use the word ki in my Aikido lessons in reference to the classic Chinese/Japanese philosophical context and try to avoid any debate on the modern interpretations or limited versions of ki.

Tom