"engine severe vibrations" would indicate the engine was not putting out full power. If you were climbing out at normal pitch, the lack of power would cause airspeed to decrease. Pitch oscillations would signal a stall. If the rudder was coordinated, those oscillations could continue until you hit the ground.
Since you turned at low airspeed and got even slower (35 KIAS), the airplane completely stalled, and the nose fell. You were VERY lucky that you pulled out before you hit the ground.