What was going on when I was born?

The Environmental Protection Agency has rejected New York State's request for $20 million in Federal funds to help clean the Hudson River by dredging chemically contaminated sediment from the river bottom and burying it. Almost all fishing has been prohibited in the river since 1975 because of the dangers of eating fish contaminated by polychlorinated biphenyls, or PCB's, a toxic substance suspected of causing cancer. For the last five years, the state, acting on its own, has sought Federal approval for the $27.6 million cleanup plan to remove some of the PCB's from the river. The plan had been recommended by a scientific advisory board.

With the Christian-dominated Lebanese Government scheduled to resume negotiations with Israel on Monday, many Moslems here are worried about what will happen if an agreement is reached to withdraw Israeli and other foreign troops from the country. Some Moslem leaders are demanding that members of the Christian Phalangist militias be disarmed to avert the threat of fighting that could lead to a new civil war. The fears of the Moslems were expressed in an extraordinary procession that took place in West Beirut last week. Hundreds of Moslems, both Sunnis and Shiites, marched, carrying banners, torches and placards proclaiming that they were an integral part of the country, not just members of another sect among the religious and regional groups that are often at violent odds with each other.

The 98th Congress convenes here Monday for a session that leaders expect to be dominated by economic questions and to be shaped by a changing relationship between Capitol Hill and the White House. The new Congress, which contains 26 more Democrats than the last in the House, comes to Washington in the wake of a special session in which both houses asserted their independence of President Reagan, who held sway over Capitol Hill for the first 18 months of his Presidency. According to statements by leaders in the House, Mr. Reagan is likely to meet substantial, even formidable, Congressional resistance in the final two years of his term. The most pressing economic issues facing the new Congress, proposed spending cuts and new taxes, job bills, adjustments in Social Security and a possible restructuring of Medicare benefits, are more broadly questions of setting national priorities, a process that the new Congress, emboldened by the November election returns, is likely to wish to share. ''We will have some initiatives of our own,'' said Jim Wright, a Texas Democrat, who is the House majority leader. ''We will not wait for the President.''

Chief Justice Warren E. Burger criticized Congress today for what he said was its failure to ease the workload of the Federal courts. He also cautioned Congress against giving life tenure to Federal bankruptcy judges. In his annual year-end report on the Federal judiciary, the Chief Justice focused on judicial administration and observed that the ''unfinished business - the accumulated and deferred maintenance - outweighs the progress.''

The New York State Legislature returns to Albany this week to confront a faltering state economy and a potential budget deficit of more than $1 billion that will largely shape - and limit - its actions in many areas. The 206th session of the Assembly and Senate, which opens Wednesday, will also face many other issues - from retraining laidoff steel workers, to requests for increased aid for New York City, to reorganizing state agencies and rebuilding roads and bridges. It will be presented with a series of proposals from the new Governor, Mario M. Cuomo, who has pledged to do more than simply balance the budget. But with the state borrowing $300 million to pay its bills this fiscal year - and facing a much larger potential problem next year - the session may put Governor Cuomo's pledge to a severe test.

''We will not wait for the President.'' - Jim Wright, Democrat of Texas, the House majority leader. (A1:6.)

Penn State was recognized unanimously today as the top college football team of 1982, the first time the Nittany Lions have been No.1 at the end of a season since they began playing intercollegiate football in 1887. Coach Joe Paterno's team, which beat Georgia, 27-23, in the Sugar Bowl on Saturday night, was voted No.1 in the final Associated Press poll of sportswriters and sports broadcasters and the final United Press International poll of college head football coaches. Penn State also finished No.1 in The New York Times final computer ranking by the widest margin in the four-year history of that selection process. And the Nittany Lions, who had an 11-1 season record, were named best in the nation by the National Football Foundation and Hall of Fame awards committee and the Football Writers Association of America.

Not even the ugly duckling, it was suggested to Calvin Peete, started from as far back as he had. "But if my recollection is correct," said Calvin Peete, "didn't the ugly duckling grow into a beautiful swan?" One of 19 children in his family--his father had married twice--Calvin Peete left school after the eighth grade in Pahokee, Fla., to help his family through difficult financial times. He couldn't do heavy or rough work because of a bent left arm that would never straighten. He had fallen out of a tree at age 12 and broken his elbow in three parts. The doctor said that if he broke it again, the arm might have to be amputated.

The Turkish judicial authorities have begun new investigations into the 1979 slaying of a prominent Istanbul journalist that they think could throw light on the assassination attempt against Pope John Paul II in May 1981. The two cases are linked because Mehmet Ali Agca, who is serving a life sentence in prison in Italy for shooting the Pope, confessed to killing the journalist, Abdi Ipekci. Mr. Agca escaped from an Istanbul prison in November 1979 before being sentenced to death in absentia for the act. Justice Ministry sources in Ankara said last week that efforts were under way to reopen the Ipekci case formally in light of new evidence from investigations in Turkey and Italy. They declined to disclose what new facts had been uncovered.

Thousands of New Yorkers lined up outside the Governor's mansion on Eagle Street today to meet their new first family. It was the second day of inaugural festivities, and Mario M. Cuomo and his wife, Matilda, opened their new home to the people of the state. For two and a half hours, the state's 52d Governor stood in the drawing room of the mansion, smiling and joking with the people. A Record Turnout Nearby, Mrs. Cuomo moved about, here standing to have her picture taken with someone, there greeting a group of schoolchildren. Outside, in chilly 30-degree temperatures, a shivering line of well-wishers stretching more than two blocks waited for hours to get into the mansion.

Swiss banks, under pressure from the United States, are warning their clients that if they want to buy or sell American stocks, they must accept the risk of having the Security and Exchange Commission told all about it. Coupled with this risk, the banks add, is the possibility that any profits from insider trading can be frozen and turned over to the S.E.C. Two of Switzerland's big three banks - the Swiss Bank Corporation and Credit Suisse - have asked their clients to sign a statement accepting or refusing the new conditions set for trading on American markets. The third - Union Bank of Switzerland -has asked only those clients who refuse the conditions to sign a declaration to this effect. But the effect is the same. The clients have been officially notified that as of Jan.1, an order for execution on American exchanges will be accepted only on the express understanding that the clients agree to possible exposure to the S.E.C. if they are suspected of trading on insider information.

High-technology companies often start with a few people working in a garage. American Bell Inc. will open for business today with 28,000 employees working in 700 buildings. Such a grand beginning is appropriate for a company that is opening a new era of competition in the telephone business. American Bell, a subsidiary of the American Telephone and Telegraph Company, was established to market telephone equipment and computerized services at unregulated prices. It is expected to bring a vast array of products to market, from office computers to computerized department store systems, able to handle such tasks as bridal registry. Starting today, consumers wanting telephones and other phone equipment will buy them from either American Bell or one of its competitors. The local telephone companies, such as New York Telephone and New Jersey Bell, will no longer provide equipment for lease under state regulation, once their current inventories run out.