For one last time, Jimmy Carter's presidency throbbed with life yesterday in White House corridors that were cluttered with packing boxes and the other unmistakable signs of one presidential staff moving out to make room for another.

With the streets of Washington jammed with happy Republicans celebrating the approaching inauguration of Ronald Reagan, the president's helicopter drifted out of a gray sky and at 12:42 p.m. set down gently on the South Lawn of what in less than 48 hours would be home for a new family.

The helicopter had brought the president and Mrs. Carter back to Washington a last time from Camp David for a dramatic spectacular climax to the tenure of the nation's 39th chief executive.

On the lawn waiting for Carter were some of the most senior and powerful officials of his dying administration -- Vice President Mondale, Treasury Secretary G. William Miller, Attorney General Benjamin Civiletti, White House press secretary Jody Powell and Lloyd Cutler, who has left his post as White House counsel but remains a key adviser.

If it weren't for all the Republicans in the surrounding streets, the people who stood gawking at Blair House across Pennsylvania Avenue where Ronald and Nancy Reagan were staying, it would have been possible to think of this as some sort of a beginning for Jimmy and Rosalynn Carter and the handful of men who met them on the South Lawn.

But it was not a beginning, it was an end. Late in the night, after most of America had gone to bed, the White House at last could announce that the agonizing 14-month hostage crisis with Iran was over, a small moment of success to climax the one-term Carter presidency that ends tomorrow.

For two long, sad months Carter had lived in the twilight zone of a defeated, lame-duck president while attention focused on Reagan, who will succeed Carter when he takes the oath of office tomorrow on the west front of the Capitol. But yesterday, while Reagan still represented the future, the president-elect was shoved into the background for a few dramatic hours. Carter, although he would soon represent only the past, still commanded the present.

In the early morning, President Carter appeared before the waiting reporters and TV cameras to announce that agreement was complete, that the hostage crisis which had so distorted and preoccupied the last year of his term was finally resolved. The 52 Americans would be coming home.

It was good news, at last, but even this final glow did not come easily to Carter. He waited and waited through the evening, his speech already written, waiting for word from the foreign capitals -- Tehran and Algiers -- which would allow him to address the nation, too late, as it turned out for most of America.

When the president returned earlier in the day from Camp David, he stepped off the helicopter and smartly returned the salute of a Marine guard. He was met by Mondale and as they walked toward the Oval Office Carter put his arm around the vice president and talked to him.

Rosalynn Carter trailed her husband off the helicopter and went immediately into the White House, perhaps to take care of the final details for moving day.

The president and vice president, followed by their advisers, marched off to the Oval Office in the White House West Wing to begin another day of meetings in the seemingly endless hostage crisis.

The Carter presidency, it was clear by then, would be a high-wire act right to the end. It was not going to end with a whimper.

And in the White House press room, the scene was eerily reminiscent of other, earlier days -- the Sunday night, for example, when the president returned from Camp David with Anwar Sadat and Menachem Begin to announce an agreement between Egypt and Israel; or another night, when he went on television to announce that the United States was granting full diplomatic recognition to the People's Republic of China.

As the meeting in the Oval Office went on throughout the afternoon, there was no real news, but the crowd of reporters and broadcast technicians grew thicker until someone observed in a slightly horrified voice: "There is an absolute gridlock of people in there. No one can move."

With no news yet from Tehran or Algiers nor from the American officials who were just a few feet away, a television camera crew filmed the reporters lounging in chairs, playing cards, or eating the hamburgers that were brought in for lunch and which gave the press room the faint but familiar odor of onions.

The Carter presidency, if not the hostage crisis, was ending in a bizarre atmosphere. On Saturday afternoon, which also had been crowded and busy but did not approach the chaos of yesterday, Powell had sat behind his desk looking at dozens of cardboard boxes packed with his papers and personal belongings.

By yesterday the boxes were gone and Powell's office walls stripped of the pictures that had hung there. His daughter, Emily, tried to nap on the sofa.

Powell's wife, Nan, was seen earlier yesterday carrying a garment bag. The sight of the bag set off a wild round of speculation that Powell, and therefore the president, was preparing to leave Washington for Wiesbaden, West Germany, to meet the hostages.

But, no, Nan Powell set the record straight. She said she had the bag because Saturday night she and her husband had slept in the Lincoln bedroom, a gesture of friendship from a president who was defeated but not quite finished.