I am currently at the point in the Face Your Fears Quest where you place the three statue items in the statue. 

The quest says "Investigate Ryngrim's Domain"... I have all the pieces required and it will not let me place the pieces to continue. I have tried loading previous saves and it still does not work.

I am at a point where I believe I will have to wait on a patch for this to continue my run. Stinks because I was enjoying this game a lot.

I had the same exact glitch. I resolved it by loading back (before) obtaining any statue pieces. You have to interact with the statue first or else that step in the quest bugs out.