What was going on when I was born?

The Mexican Government, reversing an earlier decision, said tonight that it would permit the International Business Machines Corporation to build a plant, which the company would wholly own, to produce microcomputers here. The agreement came after the computer maker agreed to sharply increase its capital investment in the plant to $91 million, from $6.6 million, over the next five years. I.B.M. also made commitments regarding the pricing of the computers, the extent to which parts would be produced in Mexico, the volume of exports and the import of technology. Negotiations on these issues have been in progress since the Government rejected an earlier proposal in January.

Orders for durable goods, buoyed by continued demand for military equipment, rose 1.8 percent in June, the third consecutive monthly increase, the Government reported today. The gain, which had not been generally expected, gave rise to cautious optimism about the economy in coming months after a year of sluggish activity in the industrial sector. The Commerce Department said orders for durable goods, items expected to last three or more years, rose to $104.9 billion in June following advances of 3.3 percent in May and two-tenths of 1 percent in April.

Late last night, as wind and rain from a tropical storm swept the puddled streets of Key West, jubilant treasure hunters and investors sang rousing choruses of ''We're in the Money'' and ''The Impossible Dream,'' pounded out by a piano player in the Two Friends bar. Besides yielding riches of silver and gold that had been buried in the ocean floor for more than three centuries, the sunken Spanish royal galleon they discovered last weekend may prove to be a scientific bonanza, their chief archaeologist said today. ''It's a virgin shipwreck in situ, one of the greatest treasure finds from an ancient shipwreck recorded anywhere,'' said Duncan Mathewson, chief archeologist for Treasure Salvors Inc. of Key West. Backers of the limited partnership spent years and millions of dollars to search hundreds of square miles of sea bottom 40 miles west of here for the remains of Nuestra Senora de Atocha, the 550-ton flagship of a Spanish treasure fleet sunk in a hurricane in 1622. On Saturday, working 54 feet under the choppy, bottle-green surface, divers found the prize. Powerful gusts of water pumped down from their ship blew up a storm of sand and exposed a jumbled mound of hundreds of silver bars, each 15 inches in length, that weighed 70 pounds each. Nearby gold and silver coins and jewels spilled from a well-preserved cedar treasure chest.

ONE of America's most renowned chefs, Paul Prudhomme of K-Paul's Louisiana Kitchen in New Orleans, gave a festive party at a Columbus Avenue restaurant Monday night to announce his arrival in New York for a five-week stay, only to be told by city health inspectors yesterday afternoon to close the premises. Mr. Prudhomme opened his roadshow version of K-Paul's yesterday anyway. ''We are not endangering anyone's health,'' he said shortly before opening. ''Our food is good and it's clean. The violations we were cited for were grossly unfair.'' When Marvin Bogner, an assistant health commissioner, was told yesterday evening that the restaurant, also known as K-Paul's, was being opened, he said that because no health inspectors were available, the department could not prevent the opening. But he said inspectors would be at the restaurant today to close it again.

Marvin L. Warner, the principal owner of the failed Home State Savings Bank, received millions of dollars in payments through fictitious securities transactions from E.S.M. Government Securities Inc., the bankruptcy trustee for E.S.M. said today at an Ohio state legislative hearing. Burton M. Bongard, the former chairman of the Cincinnati-based thrift institution, also received large payments in similar transactions, the trustee said. The collapse of E.S.M. in March led to the failure of Home State, which had heavily invested with the firm for years, and touched off the temporary closing of 71 other Ohio thrift institutions in the most extensive bank holiday since the Depression. The hearing was disrupted at midmorning by the disclosure that Stephen W. Arky, Mr. Warner's son-in-law, had committed suicide in his South Miami home Monday morning. In the past, the E.S.M. trustee, Thomas Tew, had accused Mr. Arky of receiving unusual financial benefits from the government securities firm, which was based in Fort Lauderdale, Fla.

Profusely blooming algae are turning the waters brown in parts of some bays on eastern Long Island and are puzzling scientists, who say the density and the rapid spread of the organisms is highly unusual. The blooming poses no threat to humans, according to the Suffolk County Department of Health Services. But some scientists said they were afraid the algae might have already harmed scallops, oysters and clams on the bay bottoms. ''Everything in the Peconic from Riverhead to Gardiners Island is just pea soup,'' said Dr. Scott Siddall of the Marine Sciences Research Center of the State University at Stony Brook, L.I. ''We consider this an important oceanographic phenomenon.''

Nick Molinari, a Queens parking-lot attendant, denies he is one of the richest and most powerful men in New York. But those who must beg and bargain at this time of year for a spot in his small parking lot - the only lot serving two miles of prime beach in the exclusive neighborhoods of Neponsit and Belle Harbor - insist that he is. ''Got to be!'' asserted Vinnie Picciano, who sought room in the lot. A family from the Park Slope section of Brooklyn - mother, father, baby and grandmother - was among thousands of would-be beachgoers cruising the neighborhood on a recent day, stopping every so often to plead with Mr. Molinari. ''Is there any hope at all?'' cried the mother, Angela Villanella, holding babe in arms. And after an hour or so, the 25-year-old Mr. Molinari, shirtless and tanned, took pity on them and made a space. ''Oh thank you,'' said Mrs. Villanella. ''God bless you.''

Some retailers are worried about trying to sell winter clothes in warm stores. A partner in a Manhattan law firm is sorry he installed incandescent lights when he remodeled his office a few years ago. But mainly, New Yorkers are adjusting to the latest drought restrictions on using water in the city. The most pervasive of the new restrictions, announced by Mayor Koch on July 10, affect water-cooled air-conditioners, the kind used in most commercial buildings. Temperatures in those buildings are not allowed to go below 78 degrees, and the systems must be shut down for two hours during each day, from 8 A.M. to 10 A.M. or from 4 P.M. to 6 P.M.

Companies G.M.'s earnings slumped 27.9 percent from the second quarter of last year, to $1.16 billion. But excluding a large tax credit last year, earnings were off only 2 percent. Analysts said the No. 1 auto maker was hurt by heavy modernization costs and a declining market share as shortages of popular cars held down sales. [Page D1.] Exxon profits dropped 44.8 percent, to $745 million, primarily because it set up a $545 million contingency fund after a ruling that it had overcharged customers. Atlantic Richfield had a $1.1 billion loss, after a $1.5 billion charge for a restructuring. Phillips dropped 52.4 percent, to $110 million, while Diamond Shamrock posted a $764.4 million loss, caused by a $810 million write-down. [D1.]

A dispatch from Los Angeles last Wednesday on the retirement of Timothy Cardinal Manning incompletely listed the Americans in the College of Cardinals. In addition to Cardinal Manning, they are John J. O'Connor, Bernard Law, Joseph Bernardin, John Joseph Krol, William W. Baum, Myroslav Lubachivsky (a naturalized American based in Rome) and three additional retired members - Patrick O'Boyle, John F. Dearden and John J. Carberry.

The Exxon Corporation, the world's largest industrial company, yesterday reported a 44.8 percent drop in second-quarter profits, primarily because it set up a $545 million contingency fund after a court's recent ruling that the company had overcharged oil customers. Elsewhere, the Atlantic Richfield Corporation, the nation's fifth-largest oil company, reported a $1.1 billion loss, one of the highest quarterly deficits in American corporate history. The company is going through a broad reorganization. Two other oil companies that are being restructured, Phillips Petroleum and Diamond Shamrock, also reported weak results. Phillips had a sharp drop in profits, while Diamond Shamrock reported a loss.

The General Motors Corporation reported today that its net income in the second quarter fell 27.9 percent from a year earlier, when earnings were inflated by a tax credit. Without that, the profit drop would have been only 2 percent. Analysts nevertheless termed the latest results disappointing. They said General Motors had been hurt by heavy modernization expenses and a declining market share, caused partly by shortages of some cars.