I don't know if this is what happened for you, but sometimes when Toad appears locked like that, there is a modal dialog that is hiding behind Toad (or on a 2nd monitor that is no longer there). I thought we had all of those problems fixed but maybe one is still lingering. Maybe hitting ESC will close it. Or you can move it back to the main monitor as described here: can not access main toad window - #4 by NormTeamT
If Toad is really hung (not what I described above), windows usually paints it with the "not responding" text.
I'm not really aware of anything you can do to collect data when this happens. All I know to check/do is mentioned above.
Not sure why Toad is telling me I can't recover any files when it clearly has a list of TMP files in the User Files folder!
The ~EditorBackups.txt file is the index to all of those other files (and what Toad uses to determine if there are some recovery files to show you), so maybe that file was not up to date.