* Inquiry into illegal organisation within the state
* Files opened in Istanbul and Adana
* Govt seeks to end Gulen influence over judiciary
* Gulen's movement says being demonized
By Nick Tattersall and Ayla Jean Yackley
ISTANBUL, Feb 3 (Reuters) - Turkey is launching a criminal investigation into an alleged "parallel state" backed by a U.S.-based cleric and accused by Prime ...