While operating in clouds at flight level 290, in an area with thunderstorms and turbulence, the airplane experienced a loss of power in all four engines. Information from the flight data recorder indicated that during descent from flight level 290, an elevator oscillation occurred. The #1 and #2 engines were shut down due to high turbine gas temperatures. The #2 engine was restarted before making an emergency landing at the Des Moines Airport. The captain reported that the airplane had been flown into severe icing conditions. The aircraft flight manual (AFM) prohibited flight in icing conditions above 26,000 feet (except when necessary for descent). Also, the AFM stipulated the minimum engine speeds which needed to be maintained while operating in icing conditions; it also required that the thrust management system (TMS) be disconnected in icing conditions. There were indications that the TMS was disconnected about 230 seconds after engine roll-back began. Additionally, the AFM did not provide accurate information concerning 'in cloud' correction factor for the outside temperature thermometer.