The head of the National Conservative Political Action Committee yesterday resigned in a bitter dispute with the organization's board of directors amid reports that the once-powerful PAC is in serious financial trouble.

L. Brent Bozell III declared in his resignation statement that "virtually the entire staff of NCPAC and the National Conservative Foundation have offered to tender their resignations and join me" in forming a new set of conservative groups.

Sandy McPherson, press secretary at NCPAC, when asked about its future, said: "Right now I can say I don't know, but personally, I am worried."

Bozell took over NCPAC after the death last Dec. 28 of John (Terry) Dolan, the founder and driving force of the organization. Bozell will be replaced by Dolan's sister, Maiselle Shortley, who has been on the board of directors.

In a statement, Bozell said: "Several members of the NCPAC and NCF board want to take these organizations in a direction with which I strongly disagree. I believe the results will be detrimental to the future of the organizations." He did not detail the dispute.

Bozell contended that he considered fighting for his position but "recent history has shown that such action is harmful to the movement, and easy fodder for our friends at The Washington Post. My other option was to resign and continue our programs through a new organization. Effective immediately, a new foundation, the Media Research Center, or MRC, will go into operation."

Since the 1983-84 election cycle, NCPAC has been caught in a declining financial spiral. After raising a total of $19.5 million for that cycle, revenues fell to $9.3 million in 1985-86, and in the first six months of this year, NCPAC raised only $1.06 million.

In addition, NCPAC has been carrying a $3.9 million debt, more than $1 million of which is owed to Richard A. Viguerie, the direct-mail specialist.

Meanwhile, NCPAC's sister organization, the National Conservative Foundation, reportedly has raised large amounts of money to finance extensive advertisements supporting the Nicaraguan contras and a newsletter critical of the news media.

The 1980 election marked the high point in NCPAC's history. That year, it targeted many liberal Democratic senators for defeat, spending millions of dollars on television campaigns against George McGovern (D-S.D.), Frank Church (D-Idaho), John C. Culver (D-Iowa) and Birch Bayh (D-Ind.). Those four and others were defeated, but NCPAC's role in those elections has been the subject of extensive debate.

In the 1982 election, NCPAC had little influence, and Democratic and Republican strategists generally agree that since then it has become peripheral in congressional and presidential contests.