The Arcadians destroyed and absorbed Sumner, then the Babylonians did the same to the Arcadians. Finally, the Pursians conquered the Babylonians. 'Neo-Babylonian culture' at that time would have been a provence of the Pursian Empire. Also, I doubt that something as complex and metal-intensive as a printing press would survive the sacking of a city-state. Copper was used as a form of money at that time.
WEll, it's not like this works like in Civilization. Babylonian culture continued under Assyrian, Median, Persian and Hellenistic rule, and a printing press used by its elites would continue to be used unless it was too capital-intensive (which it really isn't - it wouldn't cost more to outfit than your usual latifundium or seagoing ship). Technology tends to be transmitted rather than lost in conquests, and I can't see how the Assyrians, Medes, Persians or Macedonians would find printing useless.