The Coalition for a New Beginning came to an end yesterday -- crippled by wounds inflicted by its overly zealous backers, executed on orders from the White House despite President Reagan's claim that he had no connection with it.

Still unidentified, as the coalition closed its doors yesterday, were the contributors who had tossed $800,000 into its effort to sell Reagan's new economic program around the country. The money will be refunded, coalition officials said.

At his news conference two weeks ago, Reagan was asked if there wasn't a potential conflict of interest in the coalition's secret fund-raising efforts.

"Well, there can't be any conflict of interest, because we didn't have anything to do with it," he replied. "We know that such a program is going forward, and I have no contact with it at all. But these are the people that were so enthused after the presentation was made of the program that, apparently, they are enlisting support, just as those who are opposed to it are massing their forces together to oppose the program."

Despite the president's words, White House political director Lyn Nofziger and Elizabeth Dole, the White House official in charge of liaison with private organizations, were identified readily by White House and coalition officials as the contract points between the White House and the outside group.

And, according to informed sources, it was White House chief of staff Jones A. Baker III who stepped in last week to tell the coalition that it had to overhaul its activities or go out of business.

From the coalition's beginning of February, there was tension between Charles Wick and Justin Dart, longtime Reagan friends and members of his "kitchen cabinet," on the one hand, and the professional political organizers putting the operation together.

Wick was chairman of the coalition, and Dart was one of its most enthusiastic fund-raisers. Wick since has been nominated by the president to head the International Communications Agency, Dart has been a frequent visitor at the Reagan White House.

"The original intent was almost sabotaged by Wick," one source said. Wick and Dart had the idea of raising contributions of $50,000 from corporations. Dart was particularly enthusiastic about a planned 90-city closed-circuit television hookup on behalf of the Reagan program.

Wick and Dart were accused of making their requests in forceful ways, a source said. "He was so excited by this that passion overtook wisdom," one source said of Dart.

While the $50,000 contributions poured in, they were accompanied by a trickle of complaints that the fund-raisers were saying that a contribution was necessary to good relations with the Reagan White House.

Newsday, the Long Island newspaper that first reported the death of the coalition yesterday, quoted a presidential assistant as saying, "Wick told them that if they didn't come up with the $50,000 -- that was the coalition maximum -- then the administration wouldn't be their friend. It was way out of line."

Other coalition organizers had wanted the organization to coordinate the activities of existing groups such as chambers of commerce and senior citizens' clubs. This idea was overtaken by the high-stakes fund-raising.

The end of the coalition leaves the White House with one secret fund-raising campaign: the effort to raise money from private sources to renovate the living quarters in the White House. More than $385,000 has been raised.