my Mac Desktop does not show sound device (built in speakers) output, and sound output checkbox in mute selected. I cannot deselect it

Reset the SMC and NVRAM

Reset the SMC of your Mac - Apple Support

1. Shut down your Mac, then unplug the power cord.
2. Wait 15 seconds, then plug the power cord back in.
3. Wait 5 seconds, then press the power button to turn on your Mac.

Reset NVRAM on your Mac - Apple Support

1. Shut down your Mac.
2. Turn on your Mac, then immediately press and hold these four keys together: Option, Command, P, R.
3. Release the keys after about 20 seconds, during which your Mac might appear to restart. For example, you might hear a startup sound more than once, or see the Apple logo more than once.
4. When your Mac finishes starting up, you might need to adjust any system settings that were reset.

If all else fails to help give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.