The hurricane’s storm surge flooded the central office of Verizon on West Street in Lower Manhattan on Monday night. As computer centers in Lower Manhattan and New Jersey shut down or went to emergency operations after power failures and water damage Monday night, companies scrambled to move the engines of modern communication to other parts of the country. Others rushed to find fuel for backup power generation. In some cases, things just stopped. “Suddenly, nobody could get online,” said Arianna Huffington, president and chief executive of The Huffington Post, which went offline about 7 p.m. Monday when the computer servers of Datagram, which distribute its work on the Internet, stopped working because of rising water in Lower Manhattan.