Lawyers for twice-convicted investment swindler Cortes W. Randell, armed with letters from prominent figures praising the man they call "Cort," failed yesterday to persuade a federal judge to reduce Randell's seven-year prison term.

Randell, once regarded as one of Wall Street's "whiz kids," attracted national attention and received an eight-month prison sentence for his role in the 1970s collapse of the National Student Marketing Corp. Yesterday his lawyers went before a federal judge attempting to secure an early release from jail for Randell's conviction for a second securities fraud.

A McLean business executive who used to live in a large, Tudor-style mansion in Northern Virginia, Randell, 46, had enlisted many of Washington's elite in his cause. In the weeks before the hearing, letters had arrived at the Alexandria federal courthouse from Rep. Jack Kemp (R-N.Y.), former Nixon White House aide Charles Colson, former Federal Communications Commission chairman Dean Burch, Sen. William Armstrong (R-Colo.) and Randell himself, who said his heart and spirit "are broken."

"I've been receiving letters by the truckload," District Judge Albert V. Bryan Jr. said wryly from the bench. The judge left no doubt, however, that he was unimpressed.

Randell was convicted in his court two years ago on mail and securities fraud in the collapse of a Northern Virginia real estate investment firm in which more than 100 people lost thousands of dollars.

"He's a danger to society and he ought to be incarcerated," Bryan said, in denying the motion for a reduced sentence. "He's a con artist and he's conned some of the many, many people who wrote me letters."

Bryan also turned aside lawyers' arguments that Randell's imprisonment has caused severe emotional damage to his family. "Society's interests outweigh his very unfortunate family situation," Bryan said. "The court does not want to appear callous, but that's a side effect he brought on himself."

Randell is incarcerated in a federal penitentiary in Danbury, Conn. Defense lawyer Grayson P. Hanes said yesterday Randell will be required to serve six years before being considered for parole because of the size of the losses -- $1.3 million -- the government claims investors suffered in the swindle.

Randell's former business partner and codefendant, onetime high-ranking Labor Department aide James B. Mumford, has been released after serving a six-month prison term.

Although Randell told Bryan in his letter he has "learned an awful lesson the hard way" and promised never to engage in an "entrepreneurial type of venture again," lawyers for both sides said the former financial adviser has not been idle behind bars.

Hanes said Randell sold his 18-acre estate in McLean in November 1980 and has invested $30,000 to $40,000 of its proceeds in the commodities futures market in an effort to pay back individual investors who suffered losses in the crash of his firm.

That prompted Bryan to say he was "disturbed" by Randell's continued financial activities. "He was at Allenwood a federal correctional center when he started some of the things in this case," Bryan said.

A court document filed yesterday by assistant U.S. attorney Theodore Greenberg said Randell's latest commodities futures trading is a violation of federal prison regulations and "will be dealt with by the Bureau of Prisons accordingly."

Hanes, who disputed prosecutors' claims about how much money was lost through Randell's second company, National Commercial Credit Corp., said Randell already has repaid more than $600,000 to institutional investors.

Several persons who wrote to Bryan said they had come to know and like Randell through church activities and a Bible study group that sometimes met at Randell's home.

Colson, who served time in prison for his role in Watergate and later founded Prison Fellowship, an inmate assistance organization, asked that Randell be assigned to work 20 hours a week for the group at the District's Lorton Reformatory in Fairfax County.

In another letter, former Nixon White House aide Frederick Malek, now executive vice president of the Marriott Corp., said he had been enlisted by Randell to try to save National Commercial as it faltered in 1975.

"In all of my other dealings with Cort Randell," Malek wrote, "I have found him to be a good Christian, a devoted family man and an individual concerned with the welfare of others."