Is the music player "looking" at more than one song to choose from?
Try this:
Run the Music Player.
Choose All Songs from the list. This should show a list of all your music. (Essentially this creates an ad-hoc playlist of all the songs)
Choose the first song from the list.
Tap the Shuffle button - it should toggle between lit and dark.
If that works, then whatever method you were using before to choose a song to play was only choosing one song, so it didn't let you shuffle a playlist of one.
I was accessing the songs through my audio folder instead of through the music player itself. So you were right. I was just selecting individual songs. I wonder why it let me play through them all that way though. I could click one and it would play all of them.
Anyway, starting the music player first fixed the problem. Thank you very much.