Short version: The ship has been in hell, and is now killing everybody.
Long version, courtesy of Chris W: The ship uses an experimental black hole generator to travel the speeds needed to consider interstellar travel, a technology frowned upon because of the unknown outcome. Use of the black hole accesses a chaos dimension where the complex ship computer and the ship itself are under different physical laws, and both become "alive" in a manner of speaking. This might not be a problem in a normal ship coming back from chaos (reverting to normal after being subjected to our universe's laws), but the Event Horizon actually *contains* the black hole generator, and the events in the movie reflect the "leakage" from it.
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