More than a dozen angry residents confronted Mayor Michael Bloomberg as he visited a school in hard-hit Manhattan Beach, Brooklyn.
Mud from the storm is still piled like small snow banks in the street there.
The residents complained Monday about a continuing lack of power and heat, and about spoiled food in their refrigerators.
They also said they were afraid of burglaries.
The mayor told them the city is trying its hardest to solve all of the problems related to the storm.
He said residents can call 311 for directions to a center where they can get food and clothing.
Commuters streaming into New York City on Monday endured long waits and crowded trains, giving the recovering transit system a stress test a week after Superstorm Sandy ravaged the eastern third of the country, with New York and New Jersey bearing the brunt of the destruction.
Trains were so crowded Monday on the Long Island Rail Road that dozens of people missed their trains. With PATH trains between New Jersey and Manhattan still out, lines for the ferry in Jersey City quickly stretched to several hundred people by daybreak.
One commuter in line pleaded into his cellphone, "Can I please work from home? This is outrageous," but many more took the complicated commute as just another challenge after a difficult week.
"There's not much we can do. We'll get there whatever time we can, and our jobs have to understand. It's better late than absent," said Louis Holmes of Bayonne, as he waited to board a ferry in Jersey City to his job as a security guard at Manhattan's Sept. 11 memorial site.
The good news in New York City was that, unlike last week, service on key subway lines connecting Manhattan and Brooklyn under the East River had been restored. But officials warned that other water-logged tunnels still weren't ready for Monday's rush hour and that fewer-than-normal trains were running — a recipe for a difficult commute.
On Long Island, Janice Gholson could not get off her train from Ronkonkoma and Wyandanch because of overcrowding, and ended up overshooting her stop.
"I've never taken the train before. There were people blocking the doorway so I got stuck on the train," she said.
Bloomberg took the subway to work Monday. He was joined by many of the students returning to class in the nation's largest school system. About 90 percent of the 1,700 schools reopened for the first time since Sandy hit last Monday, the mayor said.