There are no levers to pull, no riddles to solve. Nothing like that in this section. Your whole job here is to stay alive and get to the Mantella. There are Daedra and Ghosts here. One in each room. Each room is square with three openings. There are no doors, so it's just a matter of getting through the rooms. From the room where you entered, exit to the west, go north, go west, go north, go east, go north, go north.
You're now in a dark passageway. If you look west you'll see a series of pits in the floor. Jump over them or levitate over them (levitate is best - you'll need it in a minute). Drop down the last pit and kill the Vampire Ancient if you're feeling feisty. Float down the corridor until you get to a big chamber with a shrine-looking set-up in the middle.
Float over to it. The green gem-looking thing in the center is the Mantella.
Click on it and you'll be teleported back to Nulfaga. She'll show you the result of your actions. What you see depends on who your gave the Totem to. If you came in through the front door rather than through Nulfaga, you've probably got a big problem: getting back out. You see, the only way out is through her unless you have a "recall" anchored somewhere outside.
For better or worse, you have finished the Main Quest.
From Jormungandr (16 March 2006): Almost there! Make your way through the series of chambers per usual. Once you reach the final chamber with the Mantella, you'll have to make a running jump from the threshold to the floating shrine, and then climb up one of the sides to reach your goal.
Now that wasn't so tough, was it? Got the Mantella and didn't have to use any of that silly magic stuff (save that which the dungeon provided).
Was there a point to any of this? Of course not. I just fancied a magicless character and decided that the MQ would be fun to do again, and thought I'd share the challenges of that crazy final trial Just so you know it isn't impossible without levitation. Climbing and jumping around is more fun anyways!