Zeewolf: Ah, now I know. Cruise for a Corpse.
Proof:
http://www.mobygames.com/game/cruise-for-a-corpse Good one, quite unique too. Though I never actually completed it (can't remember why).
Maybe because the apparently excellent gameplay, where you conduct a real investigation by questioning everybody on board about everything you learn (with the clock advancing each time you've done 'something good') can get confusing, and even maybe boring at a time.
Still, as you said, a quite unique game indeed, really worth the effort of completing it.
By the way, I would be so thrilled to see good old Delphine Software games here on GOG: Cruise for a Corpse, Another World, Flashback, etc...