If you think money can buy you anything, think again.

Madonna was told to get lost when she sought entry into the San Remo, a celebrity enclave on Central Park West that once housed such screen goddesses as Marilyn Monroe and Rita Hayworth.

President Nixon, after his impeachment, also got the thumbs-down when he tried to join the tenants at the kingly and publicity-shy River House, the home of his secretary of state, Henry Kissinger.

The River House, which rises 27 stories above the East River and whose tower complex offers a breathtaking 360-degree view of the city, also barred Gloria Vanderbilt, fearing that she would bring unwelcome notoriety to the building. Ms. Vanderbilt sued, to no avail. Diane Keaton, at the height of her Woody Allen movie fame, was yet another River House rejection.

Barbra Streisand, Elizabeth Taylor, and Neil Sedaka sadly discovered they were not welcome when each tried to buy an apartment at 740 Park Ave., which currently houses such well-known financial figures as a co-founder of the Blackstone Group, Stephen Schwarzman; the chairman of the New York Stock Exchange, John Thain, and the arts patron Ronald Lauder.

More intriguing insights into the Big Apple’s most prestigious residences for the rich and famous — and the co-op boards that are quick to reject millionaires, even billionaires — appear in the new book “High Rise Low Down,” a fascinating tour of the city’s classiest and most sought-after addresses.

Written by Denise LeFrak Calicchio, daughter of real estate titan Sam LeFrak, with Eunice David and Kathryn Livingston and published by Barricade Books, it will run you $24.95.

If you’ve got the bucks — and I mean plenty of them — and you want to mingle and live with the elite, Ms. Calicchio mentions a number of additional addresses with some noteworthy residents that might fit the bill.

One is 960 Fifth Ave., the pinnacle of New York luxury living with a glassed-in rooftop, stainless steel exercise setup, and, on the ground floor, an elegant Old World restaurant with a French chef. Some real estate experts consider it Manhattan’s premier residential building, housing the former CEO of Seagram, Edgar Brofman Sr.; the founder of Toys R Us, Charles Lazarus, and the Texas oilman Erving Wolf, among others.

Paupers need not apply, as no one living in the building has a net worth of less than $100 million.

If you’re an Internet buff, 820 Fifth Ave. might be just the place for your luxury abode, since you could schmooze with the CEO of Yahoo, Terry Semel. Other residents include a New York art gallery owner, William Acquavella, and the widow of Republic Bank founder Edmond Safra, Lily Safra.

Another episode in the book is the story of the battling billionaires — six, in fact — vying for the same apartment at 834 Fifth Ave., one of the city’s most coveted addresses. The rivals: Rupert Murdoch, Ralph Lauren, George Soros, Wilbur Ross, Wall Street trading whiz Steven Cohen, and major litigator David Boies.

The year was 2004, and a premier apartment at the building was on the block — the former residence of Laurance Rockefeller, a 20-room triplex with seven bedrooms, 12 bathrooms, three terraces overlooking the entrance of the Central Park Zoo, a huge library room, conservatory, and solarium.

Mr. Murdoch, anteing up $44 million in cash, eventually won out, in large measure because he had earlier lived in the building with his second wife, Anna.

The publishing magnate may have convinced the board he was eminently qualified to be a tenant, but I was told yesterday by one building resident that some tenants were infuriated that he got the green light and that some, in fact, had complained to the board about it. The reason: his divorce from his second wife, Anna, after 31 years of marriage.

Ms. Calicchio figures that entry into one of the city’s really class buildings — which doesn’t come up that often — will run you about $3 million for a small one- or two-bedroom apartment and roughly $15 million for three or four bedrooms. In such buildings, she observes, the process of getting by the board can be very tough. She recalls that one prospective buyer was once turned down merely because he unfortunately had the same last name as a board member. The way things are, she says, some board members would no longer be able to get the approval of their own boards.

One final warning from Ms. Calicchio: “Be prepared to lay out all your financial assets. It’s like stripping. And don’t ask any questions unless you’re asked.”

If that reminds you of a prisoner of war camp, I’m with you.

dandordan@aol.com