The establishment came to the backwoods yesterday to watch the twilight close in on the political career of Nelson Aldrich Rockefeller and to anoint the political future of John Davison Rockefeller IV, a "cousin" in the family hierarchy who, persistent critics claim, has an Avis-try-harder-like ambition to capture the White House for the family.

The mingling of miners with coal dust under their nails with the manicured likes of former Chief of Protocol Angier Biddle Duke combined with wall-to-wall Rockefellers to make Jay Rockefeller's inauguration as governor of West Virginia the rarest mixing of bloodlines, politics and - especially - economics in these Appalachian hills since New York's 400 finest danced with the natives inside Cudjo's Cavern at Cumberland Gap, Ky., in 1890. (That was the dedication of what the New Yorkers had been convinced would be the nation's finest resort - only it never caught on.)

While Angier Biddle Duke termed the event an excursion of the Washington "political register" - including Iranian Ambassador Ardeshir Zahedi, the Chuck Robbs, and other Washington celebrities and two governors and Julian Carroll (Ky.) and Ray Blanton (Tenn.) - Sen. Jennings Randolph proclaimed it an unprecedented affair that "puts the West Virginia start higher than it has ever been," Vice President Rockefeller acted like a retired backslapper who was for more interested in the zero weather. Greeting the new governor at a preinaugural brunch, the Vice President pulled back a button on his shirt and proudly displayed "my ski underwear."

Asked if he planned to give Jay any advice on how to be a good governor, the Vice President replied, "Ive gotten old enough that I don't give advice." Glancing around the governor's mansion, he queried Jay, "How does it look in here" I've been here before, you should have asked me how it looked."

The Vice President said attending the inauguration of a Democratic Rockefeller did not cause him to reflect on whether he too should have switched parties. "I don't look backward," he said. "I'm going to catch up with the children and Happy and the family business. I'm going to become active in promoting the American enterprise system - the greatest system in the world."

A shivering Happy Rockefeller added, "I'm going to sit in the sun and get warm at St. John's, but I doubt if I'll be able to keep Nelson quiet very long."

The other Rockefellers, however, seemed as excited and curious about the inauguration as the natives. "I'm very, very proud of Jay and very pleased for the people of West Virginia," John D. Rockefeller III, the Vice President's reclusive brother and Jay's father, said excitedly as he walked with his cane around the mansion smiling and greeting new faces. "For us it was a very new experience," chimed in Blanchette Ferry Rockefeller, Jay's mother.

Even the Carter administration people were excitedly trying to spy the celebrities. Jack Carter sonof the President-elect, was so impressed by Jay Rockefeller that he predicted, "Look for him on the national scene once Dad gets fee."

Cyrus Vance, Secretary of State-designate and formerly connected with the Rockefeller Foundation, was saying that "I wouldn't be surprised at all to see him in the Oval Office," adding that his reason for coming, however, was not because of the Rockefellers, but because "I'm a West Virginia native." Vance only laughed when asked if his presence would not contribute evidence to critics who are fond of claiming there is a Rockefeller conspiracy to dominate U.S. foreign policy.

At the outdoor ceremonies the celebrities shivered with the small crowd of about 3,500 to hear Jay's 15 minute appeal for West Virginians to "reach out . . . for your fair share of the American Dream." As he promised to end coal mine deaths and accidents, to build roads, and to place industrial development on the top of his list of priorities, the celebrities like Linda Johnson Robb - faceless behind a ski mask - visibly shook in the near-zero cold. The only warm response from the audience came when the 39-year-old Rockefeller kidded, "My name is Rockefeller, but that will not pay the bills."

That comment from Rockefeller caused a local economics professor to quickly calculate that the assembled wealth could pay the West Virginia state budget for a year out of the annual interest onit smoney. In addition to the wealth represented by the Rockefeller cousins, brothers, sisters and kin, Cleveland industrialist Cyrus Eaton was present. The 93-year-old Eaton, walking with a crudely carved wooden cane and depending on all aide to repeat a reporter's questions directly into his ear, allowed that Jay was one of the most capable Rockefellers - one who will make it to the presidency. "I knew his great grandfather John very well, and I've served with Jay on the board of trustees of the University of Chicago. He's marvelous."

Eaton joined U.S. Senate Majority Leader Robert Byrd of West Virginia in predicting Jay would do great things for the West Virginia economy. Even Arnold Miller, the president of the United Mine Workers who frequently rails against economic concentration in the energy industry, agreed with that assessment and said further, "I expect him to be the best governor we've ever had."

Miller, apparantly anticipating that the colored status card system that allocated seats based on political influence would irritate some in the audience, chose to stand at the rear instead of taking a seat up front. "It's all right back here," he said as some of the audience began grumbling that only the wealthy and influential got the coveted yellow cards that allowed their eyes to stare directly into those of the Rockefellers.

Rockefeller and his wife Sharon, the daughter of Sen. and Mrs. Charles Percy, who were also present, say they want to run an open mansion and "to never lose touch with what's on the people's minds." While admitting that their wealth creates suspicion of them, Rockefeller says, "it doesn't bother me. It's to my advantage because it keeps attention which lets me talk about what I want to talk about." His two years as a poverty worker in rural Emmons, W. Va., a political launching pad suggested to him by Charlie Peters, editor of the Washington Monthly, in 1964, and Sharon's work with a group of women artisans, have given them experience in knowing how the people of the state live, he said.

Rockefeller claims wealth has many advantages and few liabilities. "Roosevelt was very wealthy. His identification was intuitive. JFK was wealthy. His sensitivity was intutitive. It has to do with sensitivity, not a bank account." He admits, however, that he is hurt by the occasional miner's taunts, turned now into fading bumper stickers of "Remember Ludlow," a reference to the slaughter of miners in colorado by a company owned by his great grandfather.

West Virginia's new first lady, a bit flustered by her three children running through the crowd of dignitaries at the mansion, said she would not have time to settle down and move into the brick colonial mansion until "after we get back from the Washington Inaugural."

The new governor expects to be getting advice and aid from the Carter Administrationon ways to improve the West Virginia economy. He may also get an opportunity to return some advice. Asked if he would call on Rockefeller, who was a desk officer in the State Department during the Kennedy years and a fluent speaker of Japanese, Cyrus Vance replied 'I'll call on anybody who will give advice, and Jay is wise."

While much effort was devoted to bringing in country bands and other folksy things like crafts, it was clearly the craft of making money that was the major attraction of the event. And while much effort was devoted to emphasizing that Jay Rockefeller's only ambition is to be a good governor, it was his future that captured the conversations. "I think he would make a wonderful presidential canddiate," Angier Biddle Duke said. Even Republican Sen. Percy, "cold outside, but warm inside," said, "In doing an outstanding job here, how could he not go on to better things?"