Authorities began trying today to pinpoint reasons and responsibility for the blackout that crippled New York for more than 24 hours and cost millions in lost business and looting.

As businesses and public facilities returned to normal - or at least near-normal - officials and private citizens alike were asking four questions: What went wrong? Who's to blame? What was the cost? Can it happen again?

The Federal Power Commision formally opened its probe of the blackout, which began Wednesday night when lightning struck a transformer and power lines. Similar probes have been announced by the city, the state and Consolidated Edison Co. itself.

Before the federal hearing started, Richard L. Dunham, commission chairman, said the government must share the blame.

"Whatever we did obviously didn't prevent this situation," he said, referring to measures taken after the 1965 Northeast blackout. "Quite obviously something didn't fit. We're going to find out what went wrong and find out what steps can and must be taken to prevent the same thing from happening again.

"I'm satisfied that technology is available at least in the theoretical sense," he said, but "there's no way to give absolute guarantees this sort of thing won't occur."

After the meeting, however, Gov. Hugh L. Carrey said: "I can guarantee that unless we have a holocaust . . . we can prevent blackouts - because that's what government is supposed to do."

The air conditioners didn't come back on a day too soon.The temperature climbed to 96 degrees, breaking the July 15 record of 95 degrees set in 1879.

At its height, the blackout disrupted life for 9 million persons in the five boroughs and parts of Westchester County to the north and Long Island to the east. Power was restored to the last of the 2.8 million affected Con Ed customers late Thursday night, 25 hours after trouble began. The 1965 blackout lasted for 13 hours.

A state of emergency was lifted a 8 a.m. Trains and subways, which resumed limited service Thursday afternoon, carried workers through the morning rush hour. Stores reopened. Food supplies that spoiled in the heat were replenished. Court officials continued processing some 3,500 persons arrested for looting. People hurried, cars honked and streets filled as the city picked up its pace after a day of unnatural slowness.

Mayor Abraham D. Beame toured areas hit by looting during the darkness.

"Everthing's gone. Twenty thousand dollars. Not a drop left," one store owner in the Bedford-Stuyvesant section of Brooklyn told Beame.

Some residents complained that police stood by and did nothing to stop the looters. Police Commissioner Michael codd. on the tour with Beame, responded: "If each police officer went out and grabbed the first person he saw (looting), it would have meant that shortly there would have been no cops on the street at all."

Beame ecountered hostility.

"Jobs, jobs, jobs, how about some jobs, mayor," chanted a youth who confronted Beame as he emerged from a bus in Bedford-Stuyvesant. "If there'd been jobs, this wouldn't have happened. We wouldn't have to steal."

"After the stealing, then the bloodshed," a black man yelled, as Beame and the city, state and federal officials he was escorting stopped in front of the remains of a discount shoe and clothing store.

Immediately, a group of young black and Hispanic youths gathered around the officials and some 100 press people invited on the tour.

The sidewalks and streets for blocks were littered with glass and with twisted steel protective gates stripped from the store fronts.

Beame tried to explain to a store owner the various government loan and recovery plans open to small businessmen hurt by the looting. But Stanley Schalet, who operated the Nice and Pretty women's clothing store for nearly 10 years, could not be consoled.

"The police didn't try to stop the looters," Schalet said bitterly. "They took everything. Do you think anyone would want to come back here? No way." Schalet, who said he had little property insurance, estimated the clothing loss at $20,000 amd said his store fixtures were virtually destroyed.

Residents of the Area, where blacks and Hipanics blend, expressed little regret about the looting.

"So a few poor businessmen got messed up," a young man yelled at the mayor. "There's no jobs here. You should come up here more often, not when there's a disaster, but when there's no jobs and no food."

City officials estimated that more than 2,000 businesses out of some 160,000 in this sprawling city were looted and burned, but no estimate of damage would be offered by any government representative on the inspection tour.