Since the machine was in line and moved correctly when you moved it I would start suspect the overwater timer is bad.  You are correct that it should be in the second to last tower box.  The old ones were blue and white with a dial on them.  The new ones should be a solid state timer that is less prone to failure.  Since the water didn't turn off with the pivot I would suspect you also have a bad pressure sensor.  How old is the pivot and what panel is on it?  Pictures?