unable to interact with any windows, only Gnome toolbar; temporarily fixed by software suspend

After some 70+ days of uptime, during normal use, Gnome suddenly started preventing me from being able to interact with any window. No window can be clicked, Alt+Tabbed to, or focused in any way. In some cases, decorations seem to register clicks: the window gains focus, but loses it again instantly. The Meta key does not bring up the Panel, and Ctrl+Alt+arrow doesn't change workspaces. Only the toolbar at the top of the screen works. Sometimes, playing with the toolbar re-enables workspace switching, but not always.

Software suspending and resuming the computer temporarily restores functionality, then it breaks again after several window interactions.

Basically the session is hosed. This bug report was taken before rebooting. Hopefully it captures something useful, although I expect the relevant debug symbols are missing.

ProblemType: Bug
DistroRelease: Ubuntu 16.10
Package: gnome-shell 3.20.4-0ubuntu2
ProcVersionSignature: Ubuntu 4.8.0-32.34-generic 4.8.11
Uname: Linux 4.8.0-32-generic x86_64
ApportVersion: 2.20.3-0ubuntu8.2
Architecture: amd64
CurrentDesktop: GNOME
Date: Wed Mar 8 08:07:09 2017
DisplayManager: gdm3
InstallationDate: Installed on 2016-12-02 (94 days ago)
InstallationMedia: Ubuntu-GNOME 16.10 "Yakkety Yak" - Release amd64 (20161012.1)
SourcePackage: gnome-shell
UpgradeStatus: No upgrade log present (probably fresh install)