The purge of John Sears coupled with the New Hampshire landside, while renewing the conservative fathful's vitality, has neither solved Ronald Reagan's hard-core political problem nor ended brutal infighting of his presidential campaign.

The problem: stubborn belief by substantial numbers of Republicans that Reagan, for reasons of age and ideology, is sure loser to Jimmy Carter. Campaign manager Sears' efforts to solve that problem contributed to his alienation from the Reaganite grass roots, which finally lead to his dismissal by Reagan on primary day in New Hampshire.

But sacking Sears has brough neither a solution to the problem nor peace to Reagan's campaign. Rather, the internal struggle has merely changed its focus to ecomomic policy, and the departed Sears is being replaced as the center of intrigue by an equally controversial figure: former Treasury secretary William Simon.

Our spot-check of Republican Party leaders across the country showed few skeptics were convinced by Reagan's 27-percentage point thrashing of George Bush. "I'll say now what I said to you six weeks ago," one big-city Republican leader told us. "If we nominate Reagan, we lose in November." Such Republicans may now doubt Bush's viability but they have not softened their pessimism about Reagan.

Indeed, Reagan's 1980 New Hampshire vote was about the same size as his 1976 vote; the big difference was one opponent four years ago and a divided opposition this time. Thus, the New Hampshire returns did little to charm Republicans desperate for an alternative to Reagan.

Attempting to win over such critics was first among Sears' strategic objectives. But while planing down Reagan's cutting edge, Sears could not sell him to the non-Reagan half of the party. Consequently, the suave Washington lawyer became the bogeyman for Reagan's ture believers. Among conservative members of Congress who support Reagan, only two at the end has a good word for Sears: Sen. Orrin Hatch of Utah and Rep. Jack Kemp of New York.

Over the last six months, Kemp assumed Sears' old mission of trying to make Reagan credible to the non-ideological man in the street. Kemp talked Reagan into backing his tax reduction policy, which became the basis for Reagan TV spots in the New Hampshire campaign. The end product: Those voters who told poll-takers as they left the booths Tuesday that they backed Reagan because he would cut their taxes.

But, somehow, Reagan's scheduled economics speech on this theme was never made. A statement on gold convertibility, prepared by Washington business writer Richard J. Whalen and backed by Kemp, was killed on the advice of super-conservative economist Milton Friedman. Urgings by Kemp and Whalen to shift the campaign them to the average American's economic distress have not been followed.

The closest Reagan came was in the Saturday night two-man debate when he condemned Bush's acquiescence in the Carter budget's income-tax increase. Yet such debating points were drowned out by the Sears-engineered coup that isolated Bush as the culprit who kept the other candidates from debating.

On nationally televised morning programs Wednesday, a triumphant Reagan ignord conservative-populist economics as his questioners dwelled on the Sears affair. Moreover, replacing Sears with distinguished Manhattan lawyer William Casey raises questions about Reagan's economic policy.

Casey, a former Securities and Exchange Commission chairman who at age 67 is two years Reagan's junior, is closely associated with the dynamic Bill Simon. Simon not only was among the Reagan backers most critical of Sears but is a long-time critic of Kemp-style deep tax reductions and an advocate of heavy budget cuts. Whether or not Kemp and Simon end up as rivals to be Reagan's running mate, they are clearly antagonists over economic policy.

Reagan today may be only dimly aware of these struggles in his obvious joy to be rid of John Sear. They had clashed frequently in the tense days following Reagan's defeat in Iowa. Even those Reagan backers who thought Sears was pushing Reagan in the right direction believe the candidate ought to feel in control of his own campaign, although (in the words of one adviser) "it means dragging out the same old speeches and phrases."

Reagan frequently dragged them out in New Hampshire, even exhuming the Chicago "welfare queen" who had been a staple of his 1976 oratory but was banned by Sears for 1980 in efforts to broaden Reagan's appeal. With Reagan's party critics stubbornly attempting to revive George Bush or resurrect Gerald Ford, it may be too late for such broadening now, but not for more bloodletting inside the Reagan camp.