It was Saturday morning, and Dick Parsons was working out on the exercise equipment in his Manhattan apartment when he got the message. Steve Case, chairman of AOL Time Warner, wanted to talk right away. Parsons, the company's chief executive, finished his regimen, then returned the call. "Are you sitting down?" Case asked. Then he unleashed the news: he was resigning.
Parsons, 54, was surprised, especially by the timing. Everyone knew that some big shareholders, led by vice chairman Ted Turner and his friend Gordon Crawford of Capital Research and Management, wanted Case out. But Parsons had thought Case, 44,...