Apparently this glitch doesn't just exist in the XBox 360. I'm experiencing the same problem on the PC.
If you think that cheating will help, I'm afraid it probably won't. I looked up the solution on gamefaqs out of frustration, and the answer on the walkthrough I used did not work, even though the only statue to talk was saying what it was supposed to (according to the walkthrough). That means that as far as I know, this quest is essentially unbeatable, unless I am missing something.
I'm thinking this quest is required to fully upgrade my tower, or get some certain pieces of dragon armor. I was thinking it might just be a bad install until I read your post.
Does anyone else besides us have this problem? I am playing the U.S. version. I honestly can't tell if this is a bug or if they simply couldn't get all the translation done in time to get it into the game. I am also missing lines of text from the musician in the tower, and I think I've run across others as well.
I like the game so far, and I can handle a few minor glitches, but this one seems pretty game-breaking. Please please patch it!