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Chances are you have other quests to complete, perhaps the one about the Goblin City from Fedris Hler, or perhaps you've moved even beyond that.
In any case, the Dark Brotherhood is located in the sewer system beneath a trap door in one of the corners of the Great Bazaar. You won't find them immediately, but if you look around, you'll find the doors to the Manor District in Old Mournhold. Once inside, your journal will update.
There are plenty of assassins and journeymen of the Dark Brotherhood inside that are leveled to be a match with your character. Be sure to pick up their weapons as they're light and worth a lot. Make your way to Moril Manor, North building in the Manor District to find their leader, Dandras Vules. You'll have no choice but to kill him, at which point your journal will be updated. Search his body for a contract on your life that was ordered by a figure with the letter "H"... probably the King you've been hearing about.
Report your finding to a guard and he'll tell you to speak with the Captain of the Royal Guards in the Palace Throne Room, Tienius Delitian. You'll find him right above the Reception area with Effe-Tei, through a door to the throne room.
Tienius will admit to your execution warrant, but offer a worthless excuse and ask you to help him aid the King.
At this point, you can jump back and forth between a set of quests for Tienius Delitian that further the story, and some of the quests in the Temple, if you speak with Fedris Hler in the Temple Reception Area. These Tienius quests are the ones that it's possible to skip if you work your way up in the Temple quests. But why not do them at some point? They don't take long, and none require fighting if you choose not to.