What was going on when I was born?

An internal Justice Department report on the handling of the Billy Carter case has concluded that no Government official violated the law in the department's investigation of Mr. Carter's relationship with Libya. However, the report, prepared by Michael E. Shaheen Jr., head of the department's Office of Professional Responsibility and made public today, asserts that Text of the report is on page A21. the brother of former President Jimmy Carter ''lied to Government agents'' investigating his responsibility to register as an agent of the Libyan Government and recommended that the criminal division of the department decide whether he should be prosecuted. No Illegal Conduct Found ''Our primary conclusion is that no Government officials or employees have been shown to have engaged in illegal conduct,'' Mr. Shaheen said in his 10-page final report, submitted to the Solicitor General, Wade H. McCree Jr., who said he agreed with the findings.

Joe Louis, the sharecropper's son with the knockout punch, was buried in Arlington National Cemetery today, cherished in farewells at the grave and remembrances on the street corners as the ultimate champion who smashed the myth of racial supremacy. Three rifle volleys were fired across Louis's bronze-toned coffin as a crowd of several hundred watched the family and a gathering of boxing celebrities bid goodbye at Louis's open grave. The words of the New Testament saw him to rest: ''I have fought the good fight. I have finished the race. I have kept the faith.''

FOR those who dine in better restaurants, the problem is getting a reservation. But the people who run the good restaurants say that is nothing compared with their problem: People who make reservations and then, without bothering to cancel, do not show up. A check of dozens of Manhattan restaurants found that the problem had become so bad recently that many had taken drastic steps in an effort to counteract it. These measures vary according to the nature of the restaurant and its business and to the day of the week.

Shareholders paid a fond farewell yesterday to David Rockefeller, who retired as chairman of the Chase Manhattan Bank and its corporate parent, the Chase Manhattan Corporation. Mr. Rockefeller was given a one-minute standing ovation at the bank's annual meeting in honor of his 35 years with Chase, including 12 as its chairman. Mr. Rockefeller, at 65, has reached the mandatory retirement age. But Willard C. Butcher, the former president who succeeded Mr. Rockefeller as chairman, surprised the audience when he announced that Mr. Rockefeller had been named chairman of Chase's international advisory council, a prestigious group that meets twice a year and advises the bank on international matters.

The Going Out Guide yesterday incorrectly listed a performer appearing this week at Sweet Basil, 88 Seventh Avenue South. The correct performer is the trombonist Kai Winding.

President Reagan, in a move aimed at dividing Democrats in Congress on the budget issue, today embraced a $689 billion spending program for next fiscal year that is being advanced by conservative Democrats in the House of Representatives. Although some Administration officials earlier supported the conservative Democrats' alternative to the President's own plan, Mr. Reagan had made no comment on it until today. His official endorsement, in fact, came to light by accident, when Mr. Reagan became a surprise participant in a radio program in Beaver Falls, Pa. The President has been spending this week making telephone calls to key Democrats in Congress and this morning attempted to reach Representative Eugene V. Atkinson, a Pennsylvania Democrat. Mr. Atkinson, who at the time was appearing on a call-in program on station WBVP in Beaver Falls, returned the President's call, then persuaded him to go on the air.

International A decision to sell arms to Saudi Arabia was formally announced by the White House. The multibillion-dollar sale will include five Airborne Warning and Control System planes. The formal announcement, making official a decision that actually was reached on April 2, said the ''United States has made a commitment to Saudi Arabia to move forward.'' State Department officials said that following the Administration's public announcment of its commitment to Saudi Arabia it might delay for several months its formal notification to Congress, thus opening the way to a Congressional debate. (Page A1, Column 6.) Pakistan was offered arms and economic aid by the Reagan Administration, its Foreign Minister, Agha Shahi, said after two days of talks with Secretary of State Alexander M. Haig Jr. and other officials. The assistance, to be spread over five years, is being offered to offset the Soviet threat from Afghanistan. Pakistan would get $500 million in the first year, Mr. Shahi said, though Mr. Haig said no figure had been settled upon. Last year, Pakistan rejected as ''peanuts'' a Carter Administration offer of $400 million over two years. (A1:5.)

The Supreme Court ruled today that Alaska, rather than the Federal Government, was entitled under Federal law to most of the revenue from oil and gas leases issued for Federal wildlife refuges in that state. The 6-to-3 decision was a significant victory for the state in a five-year legal battle with the Department of the Interior. As a result, Alaska will obtain more than $23 million in lease revenues that have accumulated since 1976 from oil and gas drilling on the Kenai National Moose Range.

City Comptroller Harrison J. Goldin, the chief investment officer for New York City's pension funds, proposed yesterday that the funds invest $260 million to stimulate new or expanding businesses in the city and the state. Last year the Comptroller recommended the pension funds begin buying $250 million a year in federally guaranteed mortgages to stimulate the housing market in the city. The pension funds will purchase their first mortgages by July 1 of this year, Mr. Goldin said. A major effect of the new investment policy would be to provide the startup money, or venture capital, needed by growing industries in such fields as genetic engineering, computer electronics and pollution control, the Comptroller said.

Foreign Minister Agha Shahi of Pakistan said today that the Reagan Administration had offered his country a fiveyear economic and military assistance package to offset the Soviet threat from Afghanistan. Speaking to reporters after two days of discussions here, including talks with Secretary of State Alexander M. Haig Jr., Mr. Shahi favorably contrasted the Reagan Administration with the Carter Administration. Last year, Pakistan had rejected as ''peanuts'' a Carter Administration offer of $400 million over two years.

The White House announced formally today that President Reagan had decided to sell Saudi Arabia a new multibillion-dollar arms package, including five Awacs electronic surveillance planes, but that no decision had been made on when to seek Congressional concurrence. The decision on the arms package was actually made on April 2, officials said, and has been reported. But today's public statement that ''the United States has made a commitment to Saudi Arabia to move forward'' with the four-part package was the first official confirmation of that action. Officials said that the announcement was meant to reassure the Saudis that despite sharp criticism from Israel and members of Congress the Reagan Administration intended to carry out the arms sale.

A caption in Metropolitan Report yesterday on the picture of an exercise class at the St. Francis Residence incorrectly identified the woman shown at the left. She is Lolly Fountaine, a dance therapist.