 The crew attempted to pick out a path through the cells using their on-board weather radar display, but they were apparently misled by the radar's attenuation effect and they proceeded toward what they believed was a low intensity area, when in fact it was the peak convective activity point, attenuated by rain.As the aircraft descended from its cruise altitude of to near Rome VOR, it apparently entered a thunderstorm cell and encountered a massive amount of water and hail.The hail was intense enough to break the aircraft's windshield, and because of the ingestion of both water and hail, both Pratt & Whitney JT8D-7A engines were damaged and underwent flameout.