Walter J. Slaughter thought he had won his long dispute with E.I. duPont de Nemours Co. last December when the U.S. Court of Appeals for the 3rd Circuit ruled that the company violated federal labor laws when it fired him in 1978.

But Slaughter's battle was far from over.

A new conservative majority had gained control of the National Labor Relations Board. And although an NLRB administrative law judge and the board had previously ruled in Slaughter's favor, President Reagan's majority asked the circuit court last summer to vacate its decision and allow the board to study the case further. The court agreed, and the case has languished at the NLRB since June.

On Nov. 15, Slaughter will have waited six years for the government and courts to determine whether he should be reinstated with back pay as a lab technician at a DuPont plant near Wilmington, Del.

Slaughter's case was cited recently by the House Government Operations subcommittee on manpower and housing as an example of how difficult it is to resolve labor disputes through the NLRB since Reagan took office.

"Delays in decision-making at the board level and a staggering and debilitating case backlog have resulted in workers being forced to wait years before cases affecting their livelihood and the economic well-being of their families are decided," said the subcommittee chairman, Rep. Barney Frank (D-Mass.). "We have reached a point where legal rights given to employes under the National Labor Relations Act are in jeopardy because of the board's failure to issue timely decisions."

According to the subcommittee's report, which was approved by Republican and Democratic members alike, the backlog has grown from 535 cases in fiscal 1981 to 1,434 as of Sept. 1.

The "most visible" reason has been the Reagan administration's failure to fill vacancies promptly when members depart, the report said. Since December 1979, 11 persons have served on the five-member board; since August 1983, it has had only four members.

But the subcommittee said an "equally significant" reason has been Reagan appointees' attempts to rewrite existing law. The Reagan board has asked appellate courts to return 17 cases -- including Slaughter's -- that already had been decided by previous boards.

"The majority of the board has een preoccupied with reevaluating and making substantial changes in prior board case law," the report said.

An NLRB spokesman said Chairman Donald L. Dotson is drafting a response to the subcommittee. Last week, Dotson issued a statement that called the increase in pending cases "a relatively recent phenomenon . . . unrelated to the change in poltical administration in 1981." He said, "The buildup in cases began under the Carter administration in fiscal 1977 . . . . ".

The subcommittee recommended changing the law so that a board member whose term expires can continue to serve until a successor joins the board. It also said the Reagan board should stop rewriting history -- a recommendation that Slaughter said he would endorse.

Because his status at DuPont has been in limbo, Slaughter said, he has been unable to find a permanent job, receive severance pay or qualify for unemployment compensation.

"Everyone keeps saying, 'Well, you've won your case, why should we hire you?' " he said. "But I'm broke. I don't know when this will ever end . . . . If it weren't for my family taking me in, I couldn't have survived."

Slaughter had worked at DuPont for 15 years when he posted union-organizing information from the NLRB on a company bulletin board, court records show. His supervisor said he had not obtained permission to post the notice and demanded that Slaughter come to his office. He refused unless another employe was allowed to sit in. After a six-hour standoff, Slaughter was fired for insubordination.

The appeals court said Slaughter was entitled to a witness on the basis of previous NLRB interpretations of Section 7 of the Taft-Hartley Act, but DuPont asked for a new hearing. At about the same time, the Reagan NLRB issued a decision in an unrelated case that reversed its interpretation of parts of Section 7. The court asked the board if its new ruling would affect Slaughter's case. The board said it would not but asked the court to return the case anyway.

Judge Harold A. Ackerman voted against the request, saying "it appears that the new members of the NLRB seek to exercise their jurisdiction over not only those cases which come before them in the normal course but also those decided by their predecessors. This, of course, is patently improper."

Two other circuit judges voted to vacate the ruling and return the case. "We believe that our discretion is best exercised by postponing further judicial involvement until we have been informed of a comprehensive adjudication by the NLRB," they said.

The move stunned Slaughter.

"How can they flip-flop like that?" he asked. "It isn't fair."