Seems to me WW III has been going on for a while. It is being waged on different scales without common frontal assaults. It is religious, economic, cultural, political and terrorist but will grow in intensity.
Well, most "World Wars" start out as a series of separate wars that correlate as the major combatant nations join the fight. Japan was fighting in Manchuria and China in the 30's. Italy in Ethiopia. Germany was "assisting" Franco in Spain. The starting date for WW2 is generally accepted as 9/1/1939, but you could make an argument that it was already going on for several years.