On April 21, 2008, Representative Charles B. Rangel met with officials of the American International Group, the now-troubled insurance giant, to ask for a donation to a school of public service that City College of New York was building in his honor. Mr. Rangel had already helped secure a $5 million pledge for the project from a foundation controlled by Maurice R. Greenberg, one of the company’s largest shareholders and its former chief executive. And C.C.N.Y. officials, according to the school’s own records, had high hopes for A.I.G. — a donation of perhaps as much as $10 million.