Ugh, yes. Some people have a lot of problems with these doors. If the rings aren't turning, run all the way out of the dungeon (which svcks I know, that place is huge) and then go back. This will allow the game to reload the dungeon and hopefully take care of the problem. Try it a few times. You can also try to go back to a previous save and try again.
If you had the situation I had, the rings turn but the snake symbol on the key is different than the one on the door (one faces up, the other down). I've tried everything to get through that door, no luck so far.
Good news though, you can still get the Storm Call Shout without going through the dungeon. If you jump up the big half-wheel like structure in front of the cave and use the Whirlwind Sprint Shout to get to the other side of it, you can jump up to the level and just walk over and get the shout. If my memory serves me correctly, you can't use the door up there to get back into the dungeon though.
Anyway, hope this helps. Good luck!