What was going on when I was born?

As a result of cuts in Federal funds and citizen resistance to higher taxes, local governments across the country are increasingly turning to private businesses and individuals for the delivery of services usually provided by government agencies. Cities, counties and other jurisdictions are persuading volunteers to work alongside public employees; encouraging private ownership of such equipment as buses and police cars, which are then leased to the Government, and contracting to a greater degree with private concerns for such services as fire protection and garbage collecting. In Baltimore, a group of business leaders has organized ''the Blue Chip-in,'' which has been raising money to continue projects threatened by curbs on Federal funds. In New York, Metromedia Inc., the nation's fourth largest broadcasting corporation, has agreed to buy buses and rail cars from the Metropolitan Transportation Authority and lease them back to the authority to operate. And in Pittsburgh, city officials are negotiating with the United States Steel Corporation to build a bridge that it would rent to the city.

The troubled Greenwich Savings Bank, with deposits of $2 billion, is expected to be merged into two Brooklyn-based savings banks that had announced plans last April to merge with each other. The Greenwich merger would be accomplished with Federal help to keep the bank from failing. Banking sources said yesterday that the two banks were the Metropolitan Savings Bank, the 12th-largest in New York City, and the Brooklyn Savings Bank, the 17th-largest. Greenwich is the 9th-largest in the city. If the three-way merger goes through, the combined institution would have deposits of about $6 billion, which would make it the largest savings bank in New York and the second-largest in the nation, behind the $7 billion Philadelphia Savings Fund Society.

Two brothers who head a seafood union were convicted in Federal Court in Manhattan yesterday of obtaining labor payoffs in the Fulton Fish Market in a ''pattern of racketeering.'' The brothers are Carmine and Peter Romano, the leaders of Local 359 of the United Seafood Workers, which represents fish handlers in the busy market. The Government had accused them of controlling the fish market for organized crime.

A two-month-old Saudi peace plan for the Middle East originally dismissed by Washington as representing nothing new has emerged in recent days as a focus of diplomatic attention. The discussion has caused shifts back and forth by the State Department. Today, in an effort to clarify its position, the State Department said that while it welcomed some aspects of the eight-point plan proposed by Crown Prince Fahd of Saudi Arabia, ''we have problems'' with other parts of it. Meanwhile, Yasir Arafat, head of the Palestine Liberation Organization, said in an interview that he welcomed the Saudi plan because it calls for ''coexistence'' between Israel and the Arabs. (Page 6.)

Donald T. Regan, the Secretary of the Treasury, told Congress today that it was ''not probable'' that President Reagan would be able to keep his pledge to balance the Federal budget in 1984. The Secretary's comment, in response to a question at a Senate Budget Committee hearing, appeared to be a step toward an official statement that Mr. Reagan's 1980 campaign pledge could not be redeemed without hurting the economy. President Carter took a similar line in explaining why his promise to balance the budget might not be kept. After the hearing, Mr. Regan told reporters, ''I've not talked to the President in recent days on this.'' Only yesterday, the senior White House spokesman, David R. Gergen, said, ''The President is sticking firmly to the idea of a balanced budget in 1984.''

Gen. Wojciech Jaruzelski, the Prime Minister and Communist Party leader, asked Parliament today to appeal for an end to strikes. He warned that if the strikes did not cease the Government was prepared to seek a law forbidding them. General Jaruzelski, speaking nationally for the first time in his new role as head of the party, also dismissed five ministers and a Deputy Prime Minister in yet another governmental shake-up. The intent, he said, was to bring nonparty people into the administrative hierarchy.

At least seven of Manhattan's most prominent law firms are thinking of moving to Times Square as part of the proposed multimilliondollar redevelopment of the rundown 42d Street area. Such a move would establish a new center of legal practice in the city beyond those in Wall Street and on Manhattan's East Side. It also would be a major advance in the upgrading of Times Square being undertaken by the city, the state and private enterprise. The plan calls for major law firms to become condominium owners in towers at four sites: the south side of 42d Street, between Seventh Avenue and Broadway; the southwest and northwest corners of 42d Street and Seventh Avenue, and the east side of Broadway, between 42d and 43d Streets.

The Mobil Corporation offered yesterday to pay $5 billion for the Marathon Oil Company, a move that appeared to be the start of a bidding war rivaling last summer's battle for Conoco Inc. Explaining why he wanted Marathon, Rawleigh Warner Jr., the chairman of Mobil, said it was in keeping with a ''long-standing Mobil policy of acquiring and developing oil and gas assets.'' Marathon, the nation's 17th-largest oil company, has been bracing for several months for a hostile takeover attempt. It declined to make any comment, but is expected to fight Mobil's surprise bid.

The Security Council's snarled search for a Secretary General was described today as ''a deadlock within a deadlock'' by Jeane J. Kirkpatrick, the chief United States delegate. ''Any prudent person'' would now begin to look for a fresh solution, Mrs. Kirkpatrick said in an interview. ''The search for a compromise is on,'' she added. The Council, after four rounds of balloting on Tuesday and two on Wednesday, has been unable to choose between Secretary General Kurt Waldheim of Austria, who is running for a third five-year term, and Salim A. Salim, the Foreign Minister of Tanzania. The 15 members are due to meet again on Tuesday to discuss their next step, but it is not certain that they will then attempt another vote.

West Africa, Oct. 30 - Although it remains easy to come up with reasons for pessimism about a settlement in South-West Africa, the excruciatingly slow and wayward diplomatic effort to bring this vast territory to independence looked less moribund this week than at any other time in the last two and a half years. It was even possible to speak of a climate of faint hope. The Western diplomatic mission left Windhoek this afternoon in its American Air Force jet without a definite response from South Africa or the political parties here to the constitutional guidelines it presented this week. But it seemed unlikely that any of the key parties to the dispute over South Africa's continued occupation of a territory it once held on a League of Nations mandate is prepared to see negotiations break down over constitutional questions. ''People realize that this is the only game in town,'' said a senior American diplomat in the five-nation mission. His point seemed to be that rejection of the constitutional principles would mean scuttling the chance for a negotiated settlement - or in the case of the smaller political parties, of being left out if it does move ahead.

The President of Chad yesterday demanded the immediate withdrawal from his country of most of the Libyan troops whose help he sought 10 months ago to end a civil war. France, which about a week ago began sending supplies and small arms to Chad, a former French colony, publicly ''took note'' of the situation. Privately, however, French officials expressed satisfaction with Chad's move and confiremd that they had been talking with Libya in an attempt to ease the tension between the two African nations.

MOSCOW APOLOGIZES TO SWEDEN OVER SUB STOCKHOLM, Saturday, Oct. 31 (Reuters) - The Soviet Union told Sweden last night that it regretted the entry of a Soviet submarine into a restricted Swedish military zone, the Foreign Ministry said today. A ministry spokesman said the Soviet Ambassador to Sweden, Mikhail D. Yakovlev, went to the ministry last night to express Moscow's regrets. The submarine has been aground near a naval base in southeastern Sweden since Tuesday.