Three years ago John H. Bradley, a computer specialist with the Department of Defense, went over his bosses' heads to tell the White House there were grave flaws in the computer network designed to warn the president of military attack.

Bradley, who cast himself in the role of a "whistle blower," was fired from his $32,000 a year job and lost both an administrative appeal and a subsequent court case. But some of his claims were vindicated last December in a General Accounting Office study of the woes of Wimenx -- the World Wide Military Command and Control System that Bradley had worked on for five years, and that, last summer, put the nation on a false alert.

Now the mild-mannered Bethesda resident has emerged as the liveliest topic in the U.S. House race in Montgomery County where the two detail-obsessed contenders, former representative Newton Steers and Rep. Michael Barnes are always saying how much they would rather talk about "the substantive issues."

Yesterday in their respective mall headquarters in Rockville and Bethesda, Barnes and Steers' campaign chairman, state Sen. Howard Dennis, each held press conferences not to discuss energy or inflation but to argue about a television spot Steers' has been running for two weeks. The advertisement claims Barnes didn't do anything for John Bradley, a constituent. In Montgomery County, where constituents are accorded the same status as cows in New Delhi, that is close to a felony. a

In his customary monotone Barnes scored the man he knocked out of office for running TV and radio ads that exhibit a "pattern of deceit and falsehood which leaves me no option but to set the record straight."

Barnes watched somewhat grimly with his hands jammed in his striped blue suit as his media advisor played a tape of the Bradley spot that Steers has been airing for the last two weeks. The ad says that Barnes was informed that the computer network on which the president depends to react to nuclear attack is unreliable, and says that the congressman's reaction was "only silence, no letter, no call. Three times this year, the system malfunctioned. sJohn Bradley was right.He was also fired. Still no action from Barnes who was told of the danger by a constituent, yet did nothing."

"The implication is that he was fired after he brought information to me," Barnes said, calling for Steers to withdraw the ads. "Bradley was fired in 1977 before he ever came to us when his case had already been through the administrative appeals and the courts. My staff investigated the matter. We talked to the Defense Department and the Merit System Protection Board. He himself said there's not anything you can do right now."

Two hours later at the Steers' headquarters in Bethesda, Bradley stood next to campaign chairman Dennis and denied he had ever said that, adding that after an initial half hour phone call with Barnes' administrative assistant, Keith Haller, he never heard from the congressman or his office, except for one letter, again.

"I was almost desperate in talking to him [Haller]," Bradley said. "I felt I conveyed an air of desperation." Bradley said he sought Barnes' help not just to help him personally, but because the glitches in the computer system threatened the security of the country. "Barnes had a unique opportunity to address questions in a hearing. The problem is that there is a cover-up. Substantial facts have not been brought to light."

Bradley said he talked with Haller once by telephone, and never again, despite repeated attempts to contact him. Haller insists the meeting took place in his office, and says he can remember Bradley wearing a dark suit and a tie, and looking "like an algebra teacher." Of such discrepencies the campaign in Montgomery has been made.

Dennis claimed that the case was typical of Barnes' attitude toward constituent service. "This is one of the very few areas of the country where a constituent matter could involve the saving of the country. . . It dramatizes a certain issue -- Barnes is not involved in the nuts and bolts issues of his constituents."

Steers, Dennis said, has no intention of pulling the ad, and stands by its accuracy. The campaign even sent telegrams to Reagan, Anderson and Carter asking that the presidential candidates pledge to "reinvestigate John Bradley's dismissal."

Whatever response that action draws, Dennis was obviously delighted that the Steers' ad had managed to provoke Barnes. "The truth hurts," he observed. "I find his actions this morning the moral equivalent of a political nervous breakdown."