I had ArcMap 10.3.1 (or some 10.3 version) on my machine, and it suddenly stopped working. It would appear to be opening up, and then it would just crash/disappear without warning. I would see this window, and then nothing:
It always got to the same "Loading documents...." Step, and then the window would go away. Sometimes it would show up in my task bar (parallels coherence mode) but no usable windows would ever show up.
I put up with this for two weeks before I decided to uninstall all 10.3.1 programs (ArcMap, Data Interop, etc), and do a fresh install with 10.4.
I am on a one year student trial license, and here we can see everything is fine and active:
