ITCZ without an operable radar? It has happened...
IIRC, back around the 1996 time frame, an Air France 744 was scheduled to fly the Jo'burg-CDG route. Upon accepting the aircraft, the flight crew noted that the wx radar was inop. After much discussion, the decision was reached to launch, but with a massive wx deviation around the ITCZ. Approaching the line of wx over central Africa, intense lightning was observed. Crew even called up a local control tower which was reporting heavy rain and lightning. Despite large wx deviations, crew ended up flying through a CB. After extreme turbulence and in flight upset, aircraft was diverted to Nice. Structural damage as well as one fatality were the results.
As detailed in book "Catastrophes Aeriens".