The Beech 1900C, N87GL, was in its landing roll on runway 13, and the Beech A90, N1127D, was in its takeoff roll on runway 4. The collision occurred at the intersection of the two runways. The flight crew of the Beech 1900C had made appropriate efforts to coordinate the approach & landing through radio communications & visual monitoring; however they mistook a Cherokee pilot's transmission (that he was holding for departure on runway 4) as a response from the Beech A90 to their request for the Beech A90's intentions, and therefore mistakenly believed that the Beech A90 was not planning to take off until after the Beech 1900C had cleared the runway. The failure of the Beech A90 pilot to announce over the common traffic advisory frequency his intention to take off created a potential for collision between the two airplanes.