Ok, a little bit more information. After searching around on the net for sound problems, I stumbled upon alsamixer. I unmuted everything and turned up the output volume of just about everything to 50% so I'd be sure I wasn't missing anything.
Now, CD audio works fine.
But I still have an odd problem. When I choose to log off and get the "Log off", "Reboot", "Shutdown" choices, I get sound when I click on the buttons and the checkbox, plus the shutdown sound plays.
However, when in Gnome, no normal event sounds are played. Plus, when I go to Sound Preferences, I can't play the sounds through the interface.
When I try and open the sound files through Nautilus in the Sound Recorder, most of them don't play - the Sound Recorder says that their length is 0 seconds. Some of them DO play however, as they should.
Any ideas as to what is going on here?