The incident was over in a matter of minutes. But two weeks after the beating of a black motorist by Los Angeles policemen was videotaped by an eyewitness, it had led to arrests, probes by local, county and federal organizations and a Justice Department review of law-enforcement violence across the nation. It began with wailing police cars chasing a motorist through the night, cornering his car in a Los Angeles suburb and surrounding the driver as he stepped into the street. A sergeant fired a 50,000-volt Taser stun gun at the unarmed black man, then three officers took turns kicking him and smashing him in the head, neck, kidneys and legs with their truncheons. A hovering helicopter bathed the scene in a floodlight as 11 other policemen looked on. When the beating was over, Rodney King, 25, an unemployed construction worker, had suffered 11 fractures in his skull, a crushed cheekbone, a broken ankle, internal injuries, a burn on his chest and some brain damage. The matter might have ended there had not a bystander captured two minutes of the March 3 incident with his video camera. Within hours, the horrific scene was being replayed on national television. Within days, outraged protesters were demanding the resignation of Los Angeles police chief Daryl Gates. By the end of last week, four officers had been arrested for assault and 11 others were under investigation by the FBI, the L.A.P.D.’s internal affairs division and the Los Angeles County district attorney’s office. Said D.A. Ira Reiner: “It is a terrible moment, and time for serious reflection, when officers who have sworn to uphold the law are indicted for the most serious felonies.” The scandal reverberated far beyond Los Angeles, stirring a nationwide debate over excessive police violence and finally prompting Washington to take action. Last week U.S. Attorney General Dick Thornburgh announced that the Justice Department would review all complaints of police brutality received by the Federal Government over the past six years — some 15,000 cases. Though it was unclear what steps Washington might take, Assistant Attorney General John Dunne said the immediate goal was “to determine whether there is a pattern of abuse to a high degree in any particular region or police department.” Critics of Los Angeles’ Chief Gates charged that such a pattern does exist on his 8,300-member force. The day Thornburgh announced his investigation, 1,000 angry Angelenos at a police-commission hearing denounced Gates as the embodiment of a brutal, racist police department and demanded that he step down. Some in the crowd chanted, “Hey, hey, ho, ho, Daryl Gates has got to go!” Gates, 64, a rawboned, crew-cut career officer with a reputation as a law- and-order hard-liner, sat stonily through the 3 1/2-hour meeting. Though he had earlier declared himself sickened by the King beating, he said he was “very proud” of his 13-year tenure as L.A.P.D. chief and refused to resign. Said Gates: “I didn’t invest 42 years of my life to go down the tubes over an incident that I had nothing to do with.”