Old Strom Thurmond, high on the White House hit list, is running way ahead of Jimmy Carter's hand-picked candidate in a vivid demonstration of the limits of presidential political power.

President Carter's political lieutenants have bracketed Sens. Thurmond. Jesse Helms of North Carolina and John Tower of Texas as Republicans of the "radical right" who must make way for the New South. Promising all kinds of aid, the White House enlisted one of the New South's brightest faces: Harvard-educated Charles (Pug) Ravenel, who came home to South Carolina from Wall Street four years ago to win the gubernatorial nomination only to be ruled off the ballot because of residency requirements.

If the trend holds, the exercise of presidential power will have failed. Thursmond, first elected to the Senate as a Democrat in a write-in 24 years ago, has used the homely old technique of constituency service to counter ideology, charisma and the White House.

The president's motives in pushing Ravenel against Thurmond were a little clouded, centering on his private commitment to Richard Riley, his South Carolina campaign manager, for governor in 1978. That meant pushing Ravenel into the Senate race against Thurmond so Riley could run for governor.

The presidential effort included an ardent pep talk to Ravenel from Vice President Walter Mondale in the White House last year and a pledge that Hamilton Jordan, chief presidential aide, would provide uncommon assistance. Jordan was the star attraction at two Ravenel fund-raisers, one in Manhattan, one here. The president and his mother have both campaigned for Ravenel.

So Ravenel bowed to White House importuning, tackling one of the South's most indestructible political forces. Thurmond won his first election here as Edgefield County superintendent of Education in 1929 - six years before the 43-year-old Ravenel was born. By conventional standards, he ought to be ripe for plucking on grounds of age and the evolution of the South from the race wars when Thurmond was the loudest states' rights leader and an avowed segregationist.

But Thurmond has neutralized both issues. With a 33-year-old wife and four children under 8, he seems immune to the "senility issue." As for race, Thurmond has moved with the times, building a formidable bridge to the black community. He could double his 1972 black vote fo 8 percent.

That bridge has been partly constructed by Tom Moss, Thurmond's black political ace, and partly by clever constituency service. Watching Thurmond campaign last week, we saw many constituents on that bridge.

"Why will I vote for Thurmond?" a black Methodist clergyman from McCormick, S.C., said. "My boy got burned real bad 11 years ago, and Sen. Thurmond had him carried to a hospital in Cincinnati. It saved his life." That special plane belonged to the U.S. Air Force, a constituent service not available to every senator but well within the gift of Thurmond, who has been on the Senate Armed Services Committee for 19 years.

Voters of both races flock to Thurmond, who has helped a surprising number during his 49 years of elective office. To one woman he said: "How many children does Gladys have now? You haven't forgotten I offered her oldest an appointment at the military academy." In a random chat with four law students at the University of South Carolina Law School, where Thurmond was about to speak, we found three former "interns" from Thurmond's Senate office.

That may explain the findings by Thurmon'd pollster Arthur Finkelstein: a favorable rating of 72 percent (more than twice Ravenel's); an almost 2-to-1 edge over Ravenel on who would better handle economic, environmental and education issues; a better than 10-to-1 negative response to the question whether Thurmond is "a racist."

Against such polling data, any Democrat might find Thurmond a tough nut to crack. Ravenel, though feisty, articulate and highly attractive carries an extra political burden from his conduct after being removed from the ballot in 1974. He refused to bless any other Democrat for the job (telling us it would have been "hypocritical" in view of his anti-establishment campaign). In the end, the grudgingly said he would vote for his defeated Democratic primary opponent; a Republican was elected, and Ravenel was blamed.

Now he needs the Democratic establishment, but it is treating him as cavalierly as he treated it. Lacking both the establishment's help and the excitement of his 1974 upstart bid. Ravenel must pray for some sudden slip by Thurmond showing mental confusion because of age, legitimizing the "senility issue." That is beyond the power of the White House to bestow, no matter how badly it wants to get rid of Strom.