I was already in Torvald's cave on my own, but now I have to get the Crown of Barenziah out of it and the two doors where there are supposed to be Falmer coming out of them are stuck. Like, they won't open. Have tried reentering the cave, restarting the game, I dunno what to do outside of just consoling the rest of the quest which wouldn't be fun at all. Any help?

It's the section where you run into the small room with the small golden chest (dwemer chest?) and it's on a table with some gold ore and such.

Have you pulled the chain on the wall?

... What. There's a chain there? Where? Last time I went in there I'm fairly sure they opened on their own...

The same happened to me when going outside the Blackreach. Sometimes those pesky chanis and levers hide in plain sight .