I ended up breaking the high E string because using an electronic tuner and my ear, it clearly wasn't changing at all. Kept tightening the string and eventually it broke behind the nut. To look into this more I flattened the G and B strings and was wondering why the pitch wasn't changing. I looked behind the nut and see the strings are dangling while the portion of the strings that are on the fret board are as tight as before. The only thing that makes sense to me is that there is a problem with the nut, but I don't see how looking at it would help unless I took it apart...
The guitar is an Ibanez with a floyd rose.