It was an Inauguration Day like no other.

Pennsylvania Avenue was nearly deserted. Only a few diehards braved the icy winds to see a presidential motorcade serve as a wan substitute for the marchers and bands, the horses and riders of the canceled inaugural parade.

On the grounds near the Capitol there were 26,000 empty seats spread out eerily before a barren platform where President Reagan was to have taken the oath of office. Spectators huddled instead inside warm hotel rooms and crowded restaurants to do what they would have done back home -- watch it on television.

Ten miles away, the Capital Centre, instead of undergoing its routine metamorphosis from hockey rink to basketball arena, was hastily converted to presidential parade grounds. Thousands who had planned to march in the parade-that-never-was settled for watching each other in a scaled-back inaugural rally attended by Reagan. Five of the 33 bands that would have marched down Pennsylvania Avenue got to show their stuff on national TV.

And some catering trucks destined earlier for lavish parade-watching parties were rerouted to soup kitchens and homeless shelters, after many of the affairs were called off.

The villain in the piece was the weather. Bone-chilling winds and temperatures that plunged to four below zero, paying no heed to the fact that this was the nation's 50th inauguration.

They forced the president to take the oath indoors for the first time since 1945, when Franklin D. Roosevelt was sworn in at the White House. Reagan took the oath in the echoing rotunda of the Capitol. They also forced the first cancellation of an inaugural parade since it became an official part of the celebration in 1841.

But there was one thing the bitter winds could not extinguish -- a certain spirit of patriotism. There was the shivering couple on Pennsylvania Avenue waving tiny American flags and waiting an hour for the president to drive past. There were the two secretaries from Canada who stood in the cold near the Capitol and said they would "settle for just a glimpse of his car."

There were the mother and daughter, who had purchased $370 worth of gear to gird against the cold and watch the parade. But they weren't angry. "We were standing on Pennsylvania Avenue when the president went by on his way to the Capitol," said the daughter, Cindy Wright, of the District. "We waved and he waved back. It was exciting."

In his address, President Reagan spoke of the "American sound: hopeful, big-hearted, idealistic -- daring, decent and fair." Out on the streets of the capital city, people voiced the same themes.

"The economy is better . . . I don't see us being threatened anymore," said Nicholas Ornachak III, a street vendor from Johnson City, N.Y. "It is nice to be safe and it's nice to see people willing to fly the flag again."

Inside the Capitol, too, considerations of politics were brushed aside, at least for the moment.

"Everybody loves their president, whether Democrat or Republican," said Rep. Richard Gephardt (D-Mo.), often a Reagan foe. "This is an American event, where Republicans and Democrats come to honor the man elected as president of the United States."

Some, however, came for other reasons. Several hundred anti-Reagan demonstrators marched up the "Avenue of Presidents" yesterday to protest everything from high unemployment to South African apartheid.

The day ended traditionally with nine inaugural balls.

Reagan received thundering applause when he and his wife Nancy made brief appearances last night at two inaugural balls at the Washington Convention Center. He boasted about yesterday's strong rally on Wall Street and said the government would release two new economic indicators today that would show dramatic improvement.

"Sorry about the weather," Reagan said. ". . . Wouldn't you know the weatherman said that by the weekend it will be in the 40s."

Inaugural officials also planned fireworks that were to light up the sky over the mall just before midnight.

There were really two stories on this inauguration day. There was the one of the 140,000 invited guests who didn't get to see their president sworn in. The rotunda would hold only 1,200 -- all dignitaries or friends and family of the nation's leaders. There was also the story of the spirited, round-the-clock maneuver that gave the country what many called "a moving swearing-in" and later a robust rally for the 12,000 would-be paraders.

The decision to cancel the parade -- because the president was concerned that record cold "would pose significant risks to the well-being" of marchers and spectators -- came just before the Super Bowl. It caught some inaugural committee members and most of the Capital Centre's staff offguard, while they were watching the game or attending parties.

"We got a late start," said a member of the Armed Forces Inaugural Committee. "People we needed to make decisions and to start planning were at Super Bowl parties and were a little incapacitated."

At the Capital Centre, where a 6-hour switch-over from a hockey game to a circus or boxing match is routine business, even veteran workers were surprised by the suddenness of the move.

"I'm sitting here about 6:15 p.m., I got my feet up, I got my pretzels, Channel 7 [which broadcast the Super Bowl] is coming in beautifully," a security guard explained.

"Gary Handleman [director of arena administration] comes in. I said, 'What are you doing here tonight?' He says, 'What are you doing? They're moving the inauguration out here.' Twenty minutes later I looked down the road and there's a whole caravan of limousines driving up."

Capital Centre president Jerry Sachs said he was unable to estimate the price tag of the switch. John Buckley, a spokesman for the inaugural committee, said the cost would be about $30,000.

By 8 a.m., workers had finished covering the ice with 500 four-by-eight-feet sheets of plywood. A large White House communications bus, curtains drawn over the windows, was parked in the basement.

German shepherds specially trained to sniff out explosives were roaming the aisles. Capital Centre officials dropped the huge 4-sided score board, suspended from the ceiling of the arena, to the floor, and Secret Service agents scanned the inside for explosives.

ABC, which over the course of the last week placed 12 cameras at the Capitol and three along the parade route, decided to move nine cameras to the Capital Centre.

"We've been working all night," Gary Ricketts, their technical manager, said yesterday morning. "It really was a logistical thing, like taking a battalion that was attacking the eastern front and moving them to the western front overnight."

At the Capitol, a similar scene was taking place, only the players were all congressional leaders.

Sen. Charles McC. Mathias Jr. (R-Md.), chairman of the joint committee that oversees the swearing-in ceremony, at first resisted the idea of breaking with tradition and moving the ceremony inside. Then when the president personally requested it, aides said, Mathias began frantically trying to reach other committee members.

House Minority Leader Robert H. Michel (R-Ill.), one of those he called, said: "I had mixed emotions. I still argued that we should go outside. It says something about the fabric of each and every one of us. But the president felt bad about subjecting others to the cold. You know, he would have been warmed [by heaters] on the platform." And so the decision was made.

The inevitable White House limousines arrived. Suddenly, at midnight, the Capitol was alive with Secret Service agents, Capitol police officers, inaugural aides and Mathias himself.

"The hardest part was whittling down the guest list," said one committee aide, explaining that more than a thousand had been slated for front-and-center seats outside. Out went the spouses of governors, senators and House members.

Meanwhile, the phones lines were lit up until after 1 a.m., with calls from the public. "Would they still be able to come?" a committee aide said they asked. The answer was always no.

"Last week we were everybody's heroes. We had put out 140,000 tickets," the aide added. "Now we're everybody's bad guys."

Lawmakers joked about the historic move indoors. "We set a precedent we ought to follow every year," said former Senate Majority Leader Howard H. Baker Jr. of Tennessee. "Personally, I think the swearing-in should be held on the Fourth of July."

Rep. Steny H. Hoyer (D-Md.) said his wife was "ecstatic" she didn't have to sit out in the cold. "Her view of the president went up 100 percent."

Rep. Daniel A. Mica (D-Fla.) took his children out onto the presidential platform, now littered with blown-over chairs and a tarpaulin thrown over the red carpet. Each stood before the podium and took turns pretending to be sworn in. "My daughter Caroline played the first woman president," Mica said.

Along the parade route, too, most everyone made the best of the coldest inauguration day on record. Tom Florkiewicz, from Chagrin Falls, Ohio, and his family came down to do some sightseeing. "We'd never get this close if the parade were on," he said.

Ellen M. Hargrave, from Bennettsville, S.C., stood outside the Capitol, her inaugural ticket unused. "I rode 400 miles up here for this," Hargrave said. "I'm disappointed, but I'm not angry. The president couldn't control the weather. I just like to be here with the crowd."