Was it daylight or darkness? Over the sea in the dark best bet would be spacial disorientation leading to hitting the water (lots of airliners lost that way).
Engine explosion etc would probably generate a mayday call, but not for certain. More likely with headsets than handmikes (depending on airline procedure and regulation) to get a distress call off.
Rudder hard over is unlikely to bring the aircraft down on takeoff because the aircraft will be flying faster than crossover speed, so the ailerons can overpower it.
Pitot static problems might do it as well...
Cheers
Wino