Intellij IDEA 13 - Can't open Project Structure dialog anymore

This also happened to me, but removing new plugins etc didn't help.

Nor did nuking my project and rebuilding it from scratch.

In the end I deleted all caches, restarted Intellij and at last I could access the project settings again! By the way, I'm using Intellij 11.1 - mainly because I can't get 13 to start up, but that's another story

Your log shows that it is a bug in IntelliJ IDEA - they are trying to create file passing null pathname. Try to delete project files and reopen project from scratch (maybe you've lost some file) - if it won't help then you should create an issue here: http://youtrack.jetbrains.com/ - You can even copy-paste text from your question and attach stacktrace