NEW YORK — Some of society’s most vulnerable people — the elderly, the disabled and the chronically ill — have been pushed to the brink in the powerless, flood-ravaged neighborhoods struggling to recover from superstorm Sandy.

The storm didn’t just knock out electricity and destroy property when it came ashore in places like the Far Rockaway section of Queens. It disrupted the fragile support networks that allowed the neighborhood’s frailest residents to get by.

Here, the catastrophe has closed pharmacies, kept home care aids from getting to elderly clients and made getting around in a wheelchair impossible. The city has recorded at least two deaths of older men in darkened buildings.

For some living in the disaster zone, it has all been too much.

When a team of medics and National Guardsmen turned up at Sheila Goldberg’s apartment tower in Far Rockaway on Friday to check on the well-being of residents, floor by floor, the 75-year-old burst into tears and begged for help caring for her 85-year-old husband.

“This is a blessing. I’m at my wit’s end,” she said, sobbing.

Her husband, Irwin, has a pacemaker, wears a colostomy bag and needs her help to do almost everything. When the power was on, Goldberg said, “I could take care of him by myself and survive.” But for days, the building had no heat or electricity. There were no open stores to buy food. Until the end of the week, there was no water or elevators either, meaning residents like the Goldbergs, on the 25th floor, had to cart water up the steps themselves just to flush the toilet. A bad stench permeates much of the building.

“I’m running out of my blood pressure medication. We’re both going to drop dead in this apartment,” Sheila said. The medical team said it would make arrangements to transfer Irwin to a medical facility, at least temporarily.

City and federal officials, and a growing army of volunteers, are trying hard to make sure families like that don’t fall into despair. Their efforts come alongside relief workers, donations, volunteers and demolition crews who flocked to New York and New Jersey in recent days to assist in the massive cleanup. The region took a few more steps to move past the storm Saturday, when power was restored for many more and gas rationing eased some of the clogged lines at stations in New York.

Paramedics from all over the country, including the ones that found the Goldbergs, fanned out across the Rockaways this weekend to check on shut-ins and anyone else who might need help.

The idea was to find people who “sheltered in place” during the storm, who might need assistance, said Nancy Clark, an assistant commissioner in the city’s health department.

The going was slow. In their first three hours, the teams had gone through five high-rise towers. Several people were taken to the hospital. Others were hooked up with water, food, blankets or needed prescription medications.

Two floors below the Goldbergs, medics from South Carolina found Daisy Nixon, 70, slumped in a chair under a pile of blankets. A diabetic and a victim of two strokes, she was suffering from an untreated dislocated shoulder injured before the storm. Nate Thompson, an EMT, checked her blood glucose levels and found them troublingly high.

“It’s been cold. Lord, have mercy,” Nixon said. She said she was also having trouble breathing at night. When Thompson said he would get her an ambulance, Nixon was overjoyed.

“Can I kiss you? Don’t you walk away from me,” she said, and planted a smooch on his cheek.

Another neighborhood resident, Joseph Williams, said that the home care aide who normally helps look after his 27-year-old son, who has cerebral palsy and needs a wheelchair, hasn’t been able to visit since the storm. After days of trying to take care of him himself, in a flooded high-rise with no utilities, Williams gave up and carried him down seven flights, so he could be evacuated to Brooklyn.

Yet, there were rays of hope amid the gloom. In Newark, N.J., an Amtrak train arrived pulling a box car filled with donations from New Orleans.

Fuel lines in the region remained long, but were only a shade of the nightmare they had been in recent days. Some gas stations on Staten Island had 20 cars in line Saturday afternoon.

In Staten Island’s waterlogged New Dorp section, volunteers walked in knots, often carrying shovels and pails with the price tags still on them. A Boy Scout troop served hot dogs and grilled cheese. People pushed grocery carts filled with food and bottled water. On one sidewalk, a generator was hooked up to a popcorn maker, spilling a fresh batch into a bowl.

Mandie Collins and Mary Lou Sabatini, from the West Brighton neighborhood of Staten Island, cooked a turkey and ham, and walked door to door with coolers offering sandwiches.

“It’s surreal,” Collins said. “I lived down the block before. I passed by my old apartment and it’s gone.”

Utility companies have made progress restoring power. Most service was expected to be restored in New Jersey over the weekend, and the utility that serves New York City and suburban Westchester County said it has restored electricity to about 99 percent of the 1 million homes and businesses that lost power in the storm and a subsequent nor’easter, though that percentage doesn’t count tens of thousands of homes the utility says are too damaged to receive power.

Power problems remained unresolved on New York’s Long Island, where about 300 people staged an angry protest at an office of the beleaguered Long Island Power Authority. About 130,000 of its customers still didn’t have power Saturday, LIPA said.

Amid the drudgery and heartbreak of cleanup came one special moment for Joanne McClenin, who had 5 feet of water in her Staten Island home.

On Wednesday, her husband returned to their house to find someone had returned Joanne’s 1930 baptism certificate from St. Anthony’s Church in Manhattan. It had a smudge of mud on it.

The certificate had been stored in a file cabinet of her late parents’ belongings, stored in a shed in their yard. The water from Sandy swept it away.

“It felt like my father was watching me,” she said.