In short: try just type your password, press enter. This worked for me and I had all of the same symptoms:
- UI will completely freeze: x
- except the mouse will move: x
- won't respond to any clicks or keyboard: x
- not even ctrl+alt+delete: x
- music will continue play: x
This won't answer "how to debug this" but it may get your computer usable without having to resort to killing anything, so that you can begin to debug this.
You are not telling us if this happens suddenly while doing something, or if it happens if you leave the computer for a little bit.
In my case, this happens if I leave for a short time. I.e. when I come back, the screen looks exactly as when I left it and it won't respond to anything - yet I can move the mouse.
What I found out is that for some reason it is only rendering that frame over and over, however beneath it is all active. It is actually prompting me for a password and all I need to do is enter it in the dark and then it is all functioning again.