This is new behaviour. I should be able to select a group by clicking anywhere within its bounds and the group as a whole would be selected. Now each object acts as if it were not grouped. I did find a workaround, but it doesn't make sense. If I select all objects and group them, thereby making a group within a group, then clicking within the group selects everything as one object. This is stupid and I have no idea what I did to cause this behaviour. It was working yesterday and I haven't updated the program! What is going on?

Likely you have accidentally entered the group by double clicking on an object in the group, or via the Objects/Layers dialog... this will exhibit the behavior you describe. 

The Status bar at the bottom of the screen will indicate what layer or group you are working in.

http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Groups.html

Thank you! That did it.