Two people died and two were injured in Boston because of carbon-monoxide poisoning linked to the storm, which dumped up to 30 inches of snow on the state. Hundreds of coastal residents were evacuated from the North Shore to Cape Cod, and more than 400,000 people in Massachusetts awoke without power Saturday.

Begrudgingly but steadily, conditions improved throughout the day as power slowly returned and traffic-free streets became cross-country ski tracks. Governor Deval Patrick lifted the statewide travel ban at 4 p.m., 24 hours after imposing the first such prohibition since the deadly Blizzard of ’78.

“We still have a little way to get through the rest of the storm,’’ Boston Mayor Thomas M. Menino said. “Please take care of one another.’’

Despite its shimmering veneer, the snow continued to cause significant problems. Public transportation remained at a standstill in Boston and its suburbs, and the MBTA said it is trying to restore service by Monday morning.

Amtrak canceled train service to New York, and runways at Logan International Airport, which recorded hurricane-force winds of 76 miles per hour and 24.9 inches of snow, were not expected to reopen until at least 11 p.m. Saturday. The US Postal Service suspended mail delivery.

The snowfall, the fifth-largest to be measured in Boston, approached the city record of 27.6 inches set in 2003. The Central Massachusetts town of Spencer recorded 30.5 inches, apparently the highest in the state.

Elsewhere in New England, more than 38 inches of snow fell in Milford, Conn., and a gust of 82 miles per hour was recorded in nearby Westport. In Portland, Maine, 29.3 inches of snow fell, eclipsing the record set in 1979.

Carbon-monoxide exposure killed a boy in Roxbury and a man in Mattapan, both of whom were overcome Saturday while sitting in running cars with tailpipes blocked by snow, authorities said. The unidentified boy, believed to be 14, had been shoveling snow in the morning before he sat in a car to take a break, Fire Department officials said.

In late afternoon, an unidentified man in his 20s was found dead inside a car on Woolson Street in Mattapan.

Shortly afterward, a 7-year-old girl and her 4-year-old brother were taken to the hospital with carbon-monoxide poisoning after being found in a car on Porter Street in East Boston. The children are expected to survive, authorities said.

“People have not seen this much snow in a long time. They’re not focused on making sure they clear the snow from the exhaust pipe before putting anyone inside,” said Cheryl Fiandaca, the Boston police spokeswoman. “Carbon monoxide fills the car pretty quickly.”

Although the National Weather Service had yet to formally declare the storm a blizzard, it certainly felt that way to many people. About 50 people had to be rescued from cars stranded during the storm, mostly from highway ramps.

Along the storm-battered coast, many residents continued to suffer Saturday. In Salisbury, more than 40 people were evacuated from about a dozen homes because of flooding. A mandatory evacuation order had been issued for 1,000 people in the densely settled beachfront neighborhood.

“One tide went right through the surf side” of a home, said Salisbury Police Detective Steve Sforza. “They said the ocean was inside their house, and they were right.” Four adults and two cats were taken out.

On nearby Plum Island in Newbury, the building commissioner determined that six homes could not be occupied because of beach erosion.

In Quincy, which lost nearly all power, flooding forced dozens of people from their homes. Dozens more sought warmth, food, and a bed in emergency shelters set up at the two city high schools. By Saturday night, some of the power had flickered back to life.

Elsewhere along the South Shore, the National Guard helped rescue residents in Hull and assisted local officials in the hard-hit coastal communities of Marshfield, Scituate, and Weymouth.

In Scituate, a tidal surge breached a sea wall Saturday morning, sending water pouring onto streets and spurring frantic calls for help on Saturday morning. “I was just with the chief of police, and right now every other call is an evacuation,” said Anthony Vegnani, vice chairman of the Board of Selectmen.