The several circuit courts of the State and, except as otherwise provided by statute or rule, the several state district courts, subject to appeal as provided by law, shall have original jurisdiction to hear and determine the following matters, and, unless otherwise provided by law, shall determine all questions of fact involved without the intervention of a jury:
(1) All claims against the State founded upon any statute of the State; upon any rule of an executive department; upon article I, section 20, of the Hawaii State Constitution; or upon any contract, expressed or implied, with the State, and all claims that may be referred to any such court by the legislature; provided that no action shall be maintained, nor shall any process issue against the State, based on any contract or any act of any state officer that the officer is not authorized to make or do by the laws of the State, nor upon any other cause of action than as herein set forth; and
(2) All counterclaims, whether liquidated or unliquidated, or other demands whatsoever on the part of the State against any person making claim against the State under this part.