Actually, that's not quite true.  The earliest mention of Babylon is with the reign of Sargon the Great, circa 2234 BC.  The earliest Greek civilization is believed to be the Minoan civilization from around 2600 BC.  Although there is no generally accepted system of Bible chronology, most scholars of ancient history place the time of the Great Flood at somewhere around 2348 BC, although I suppose it is possible that all three civilizations wrote their own accounts of the event. 

As far as the age of the earth is concerned, radiometric dating methods (carbon-14, etc.) only work with things which were once living, i. e., it cannot be used to determine the age of geological formations.  Furthermore, when one understands how carbon-14 dating works, it is easy to see that calibration of the carbon-14 clock outside of the period of recorded history is not possible.  Therefore, your estimate of when the dinosaurs existed is not valid.

Sorry to confuse you with facts; didn't want to run the risk of boring you with all that "fundamentalist garbage".