You sure you killed the duke? As I recall it's the boss of the imperial legion who gives you that quest. Duke Dren is the Dunmer guy standing next to him.
The legion boss isn't essential to the main quest. I can't remember if Duke Dren is needed, probably depends on whether or not he's involved in you being named Hortator by house Hlaalu.
Then again, if you had killed anyone essential you should have been warned by the game anyway; (a bit of text about "threads of the prophecy severed blah blah").