Skyrim Secondaries- Forbidden Legends: Threshhold of Power
This new room you've gained access to contains a powerful Draugr Scourge, one that likes summoning atronach to attack you while it stabs you with its sword. Ignore the atronach in favor of killing the scourge and you won't have too much trouble. There is also a trap trigger plate on the floor near the far door, which will operate a soul gem powered trap- thankfully, the gem is in plain view and once you take it the trap is inert.
Set the three pillars here to match the key heads in the opposite room, then return to the room with the two thrones. This time, when you pull the chain, you are rewarded with an open stairwell rather than a poison dart to the head. Descend the long wooden spiral stair to the bottom, where you'll find shallow flooding in the deepest layer of the tomb.
Advance carefully, for here there be spiders- a pair of frostvenoms, one large and one small. Empty out the burial urn on the stairs, then stop before entering the hall with the locked ring door. You'll notice that this hall is different from the others you've seen so far- a series of sarcophogi line the walls. These are guardians of the room, and a cluster of draugr of varying levels you'll have to kill to get to where you're going. Their eruption from their entombment is triggered by someone entering the center third of the room, so if you're canny (or just mean) you can send your follower in first.
The draugr tend to be present in pairs, emerging in the order of ordinary-ordinary-restless-restless-restless-ordinary. Slay the lot of them and make sure you wait for the lighting to return- that's when you know you've finished the job. A sneak archer or thief with appropriate Sneak damage skills can easily murder the draugr as they escape their crypts, before they can attack, but it's virtually impossible to be fast enough at it to kill all of them in complete safety.
Once the six draugr are dead again, check the Ivory Claw's palm for the solution to the door- Eagle Eagle Dragon. The small hallway following the door contains a little bit of loot and some discarded gear- and the door at the end leads to your goal here, Folgunthur Crypt.