I log in as my normal user, and I discover that I no longer have the option to power the computer off or switch users.

Also, oddly, the sound package doesn't load.

I log in as root, same issue. Any ideas?

So just the Power icon in the taskbar is missing? Gues can just use "poweroff" and "su" command until you find fix

Maybe a recent update or misconfiguration has jacked things up on ya because Ive never heard of that happening....could always try the "apt-get -f install" or "apt-get update && apt-get dist-uprade" al last resort

Sound could also be fixed with the "pulseaudio -enable" to manually start it up or "systemctl --user enable pulseaudio" to change the config file to start backup at boot up

Which version of CentOS are you using?

Which desktop environment/window manager are you using?

Are you using sudo or do you have the normal root user account with an un-privileged account?

Can you use the CTRL + ALT + F* keyboard combination to get to a CLI and run the su command? (the + sign is not a part of the keyboard combination)

CentOS v6. I can su or log in as root. Are you asking if I dorked something up as root? It's possible, but I don't think so...

What happens when you run, as root, the cmd: poweroff ?
Maybe investigate via: strace -f -o myfilename poweroff

Let us know more troubleshooting details.

No, I was not asking that, we need a clearer picture of your system. So, I take it you are not using sudo?
You did not say what desktop environment you are using or if the keyboard combination works or not.

Do any command-line commands power-off your system? (eg. the poweroff command)
Has anything changed since the last time it did work? Has it ever worked?

Is there any reason why you are still using CentOS 6? The latest version is CentOS 7.4

Unless you have any particular reason for using CentOS 6, I suggest you look at upgrading to CentOS 7.4

We need more details to help you with your problem, as there is nothing I can even suggest, based on current information supplied.