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Gnome desktop almost totally unresponsive in Jessie

I've got a small problem. On our local Jessie box, the Tomcat and Apache web servers both seem responsive enough, and I likewise have no trouble getting and using an SSH session remotely (except that the "find" command is extremely slow).

But the Gnome desktop has become almost totally unresponsive.

I'd rather not restart the box. Any advice on how to deal with this without restarting the box?