Union Station, the colossal train terminal that has crumbled and closed under 15 years of bungled stewardship by the federal government, yesterday was granted a $70 million reprieve by the U.S. Department of Transportation.

Transportation Secretary Elizabeth Dole, speaking yesterday beneath a water-stained white granite arch in front of the station, said the money will be used over the next five years to turn Union Station into what it was before the government got involved--"a living building, alive and vibrant with people."

When Congress first got involved with the station in 1968, former Rep. Kenneth J. Gray (D-Ill.) promised on the floor of the House of Representatives that "the proposal we bring to you today will not require one cent of taxpayer's money . . . "

But with yesterday's pledge of $70 million, the total commitment of federal money at Union Station--turning it from train terminal to National Visitor Center and back to a train terminal, while building an as-yet uncompleted parking garage--comes to $258 million. It was built 75 years ago at a cost of $21 million.

As a kind of step-child of Congress and the federal government, the station was the victim of wishful thinking by members of Congress, of huge cost overruns and of bureaucratic infighting between the departments of Transportation and Interior.

The station, after its conversion to the National Visitor Center, had a "pit" dug in its main waiting room to create a slide show theater. The slide show was unsuccessful and the pit, which cost $1.6 million and was widely condemned as damaging to the building's architectural integrity, was closed five years ago.

Federal Railroad Administrator Robert W. Blanchette said yesterday the pit will be covered over and the station's main waiting room once again will be furnished with seats. "You will never see the pit again," he proclaimed.

The station's leaky roof, from which large chunks of plaster began falling two years ago, forced the station to be closed for safety reasons in February of 1981. The leaky roof was ignored in the early 1970s, as the government elaborately renovated the interior of the station at a cost of $9.1 million. Water intrusion has destroyed most of that renovation work. The U.S. Park Service, at a cost of $9.7 million, is still fixing the roof and will not be finished with the job until late 1984.

Officials who gathered at the station chose not to speak of the building's history. Instead, proclaiming new optimism, they spoke of the future.

"With this agreement we are preserving an historic structure, we are restoring the building to its original transportation purpose, and we are providing Washington with a new commercial center with exciting economic potentials," said Dole, who is the ninth secretary of transportation to wrestle with the issue.

"This is a great day for Amtrak," said W. Graham Claytor Jr., the fourth president of Amtrak to covet a restored Union Station as the southern end of the Northeast Corridor train line.

"It's time to get an eyesore in the nation's capital in shape," said Mayor Marion Barry, who has pledged $40 million of previously appropriated federal highway construction funds for the uncompleted parking garage behind the station.

The 1,296-car garage, left to rust in the early 1970s because of cost overruns, is expected to be completed in three years, according to Dole.

The $70 million from Amtrak and DOT also is previously appropriated money available because of savings on other construction projects and from other sources.

The station will be open to the public in 1988, according to FRA administrator Blanchette. He said it soon will be leased to a developer who will help transform the station into a "marketplace" similar to Harborplace in Baltimore or Faneuil Hall Marketplace in Boston.

Before the station is reopened, the so-called "replacement station" now used by train passengers will be destroyed. Tracks will be returned to the station's concourse "so passengers don't have to walk a long distance to the trains," Dole said.

Once the building is renovated for a developer, Dole said, "the private sector will take over. The DOT will continue to oversee the building, but then it will become a showcase of the Reagan administration's faith in private sector initiatives."

Among all the hopeful proposals mentioned yesterday by officials, who stood near a "Closed For Safety Reasons" sign on the station's front door, the one that most immediately will affect train passengers is a plan to construct a new walkway to the trains. The walkway, costing between $200,000 and $300,000, will allow passengers to reach the trains without walking 400 feet around the outside of the closed granite building.