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Living conditions remained severe for tens of thousands of people unable to return to their homes, and some 1.4 million homes and businesses were due to endure another night of near-freezing temperatures without power or heat.
The devastation could also send ripples through Tuesday's presidential election, with President Barack Obama and Republican challenger Mitt Romney locked in a close race.
An exhausted region now faces the prospect of a new storm. A strong "Nor'easter" was forecast to bring freezing temperatures and more rain and wind by the middle of the week, possibly flooding coastal areas that have yet to recover from Sandy.
The US death toll rose to at least 113 and thousands of homes were destroyed or damaged by the gigantic storm, which slammed into the US East Coast a week ago, bringing a record surge that flooded low-lying areas with seawater.
Hurricane Sandy killed 69 people in the Caribbean before turning its 130kmh winds on the United States.
Most of New York City's 15,070 schools reopened but 57 suffered structural damage and needed to be relocated, 20 lacked power and another 16 were closed because they were being used as shelters, the Department of Education said.
With sizeable legs of the region's public transportation network still hobbled by storm damage, people stood for an hour or more on train platforms or street corners in New Jersey, Long Island and Connecticut waiting for trains and buses, only to find many of them too crowded to board.
Service on many rail and bus lines was reduced and the New York City subway was running at about 80 percent of its normal service.
The commute from New Jersey was particularly trying.
As a Northeast Corridor Line train on the New Jersey Transit network pulled into Newark, passengers wondered aloud how the hundreds of people who crowded the platform would squeeze into the already-packed train.
A conductor banged on the window, signaling passengers to squeeze together more than they already were. "Move in! It's gonna be a tight fit," another conductor yelled. Still, there was no room for about half of the passengers.
"I'm taking Amtrak back this afternoon, so I don't have to deal with this," said Gabrielle Nader, 27, a human resources professional who boarded in Trenton. "It's worse than a subway."
Hundreds of commuters tried to get ahead of potential logjam on NJ Transit's commuter rail by flocking to national carrier Amtrak, which sold out rush-hour trains through Friday along the corridor. Amtrak prices can run more than twice those of commuter rails, adding to the economic hardship of those affected by the storm.
ELECTION DAY CONCERNS
An estimated 30,000 to 40,000 people in New York City were in need of shelter, including 20,000 in public housing, New York City Mayor Michael Bloomberg said on Sunday.
Some 750 construction workers resumed rebuilding at the World Trade Center site known as "Ground Zero" since the attacks of Sept. 11, 2001. Sandy's record storm surge caused the Hudson River to pour into the Sept. 11 memorial and museum and temporarily stopped construction on two skyscrapers that have nearly topped out.
Concerns were also growing that Sandy would prevent displaced voters from reaching polling stations on Tuesday. Scores of voting centers were rendered useless by the record surge of seawater in New York and New Jersey.
New Jersey has said it will allow people displaced by the storm to vote by email. In New York City, some 143,000 voters will be reassigned to different polling sites. Both states are normally easy wins for Democrats.
PSE&G, the largest electric utility in New Jersey, said early Monday it had restored power to 78 percent of the 1.7 million customers blacked out by the storm.
In New York, utilities came under increasing pressure to restore heat and light to some 650,000 customers. More than half of those were served by the Long Island Power Authority, which was singled out for criticism by Governor Andrew Cuomo.
Tab Hauser, deputy mayor of the still-dark Village of Flower Hill on the north shore of Long Island, said that not only has the cleanup been too slow, Long Island Power Authority "is doing nothing to prepare for the future."
He would like to see the utility consider underground lines and metal rather than wood poles. "Every year it's a Band-Aid," he said. "This can happen next year and nothing will change."
Lee Green, 45, a firefighter who owns a property management company in Westhampton Beach on the southern shore of Long Island, said there were parts of the coastline "where the dunes are just completely wiped out and there's a 20-foot (6-metre) drop from the back of the homes to the beach."
He said the fire department had been deluged with dozens of emergency calls around the clock. "Wires down, road hazards, car accidents, telephone pole fires, alarms going off," Green said.
"The power grid out here is really old and quirky. And when it shorts out, it causes chaos all over town."
After a peak of 8.5 million outages across 21 states affected by the massive storm, the rate of restoring power each day has slowed as line crews must work on increasingly difficult and isolated outages.
The New York Harbor energy network was returning to normal with mainline power restored, but there were concerns about heating oil supplies with cold weather forecast.