WHEN a Boston bank crushed 200 out-of-date computers earlier this year, Alex Randall cried. "It kept me up nights," he recalls.Did it really keep him up? "Oh yes! Yes. I am on a mission," says Mr. Randall, sweeping a hand toward one of the many computers at his desk. "The covert message of this thing is: 'You are a free thinker. If you thought computers were boring, you never met Alex Randall. He has turned his 10-year-old venture, the Boston Computer Exchange, into a bully pulpit. Call him the king of used-computer salesmen, the guru of technology transfer. His message is as simple as the "Pass it on" button he gives to his guests: The aging machine in the corner of the office is too good to throw away. "My ideal is for the computer to be donated by the corporation to the school, from the school to Czechoslovakia, from Czechoslovakia to the Soviet Union," and so on, Randall says. He stands in a unique position to do this. As head of the Boston exchange - the first such computer exchange in the United States - he oversees the transfer of thousands of used computers a year. The exchange links up buyers and sellers. Some of the used machines come from individuals, others from corporations, and still others from manufacturers with unsaleable items. He also heads up the 10-month-old East West Education Development Foundation, which takes old, unmarketable computers and donates them to schools and institutions that foster East-West understanding. So far this year, the foundation has sent computers to Russia, Bulgaria, and Czechoslovakia. CYNICS might find this faith in computers misplaced. Technology can do bad things, too. Don't engineers use computers to build and guide missiles and bombers? "Let 'em!" he shoots back. "It's inherently liberating." The same technology developed to guide missiles is used to land planes at airports. Early on, the computer industry spent all its time building newer, better, faster machines, he says. It convinced businesses and individuals to buy them but never gave any thought to what would happen to the old machines. In 1982, he founded the exchange with his wife, Cameron Hall, completing dozens of trades a month. He recalls crawling over equipment scattered around his apartment, trying to match yellow and blue cards of buyers and sellers: "I was getting out of bed and stepping over keyboards." Now the idea has blossomed. With some 20 employees working out of two buildings just off the Boston Common, the Boston Computer Exchange brokers thousands of transactions a month. Hundreds of similar exchanges, inspired by the Boston model, have popped up around the country. Even computer companies are coming on board. International Business Machines recently began taking trade-ins from buyers of new machines. Inacom, a large computer dealer nationwide, has started TechTrade - a program that gives corpor ations a chance to trade in old machines for new ones. Inacom signed a deal with Boston Computer Exchange a year ago and has tripled the number of units the exchange handles. Still, for every completed trade there are eight potential buyers who go away empty-handed. Randall is organizing a national network of computer exchanges to give buyers a larger market. When Randall started the Boston Exchange, the IBM PC computer was displacing an array of older machines. In August, it was the PC's turn to be put out to pasture. Its price had fallen to $200 - not worth the 15-percent commission that the exchange charges - and is now accepted as a donation item only. But as donations, these machines still have a long life ahead of them - especially in Eastern Europe and the Soviet Union. The East West foundation has sent laptops to the foreign policy school in Moscow run by former Soviet foreign minister Eduard A. Shevardnadze and to journalism students in Moscow, St. Petersburg (formerly Leningrad), Prague, and Bratislava, Czechoslovakia. THE biggest problem right now is not finding donors of computers - NEC Technologies, Gillette Corporation, AT&T Bell Laboratories, and others have given equipment - but donors of transportation. It costs about $4,000 just to rent a container for a transoceanic shipment, he says, and he needs two containers to ship the roughly nine tons of equipment in his warehouse. Randall's fervor about computers has not gone unnoticed. "His name was the first one I thought of to call," says Patrick McGovern, chairman and founder of International Data Group and the man who established the East West foundation. "I had known Alex Randall for quite a while. He had the passion and the enthusiasm in the mission." Randall had traveled previously to the Soviet Union to try to sell some of the exchange's computers. It was one of his less successful trips: lots of enthusiasm but no money. "I didn't get 50 cents," he groans. When he announced he was giving away free diskettes at a trade show, his booth was mobbed. Some of the donated machines are so outdated - they precede the IBM PC - that even Randall has wondered whether the Soviets could use them. But "they say: 'Bring it over. We will find a use for it, he says. And from the looks of things, Randall will keep supplying their needs. "I want to see these machines in the hands of those kids. A Czech kid sitting at a computer is a business waiting to be born."