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First reset the System Management Controller of your Mac. Follow the steps below;
Shut down the computer.
Unplug the power cord and also disconnect all other devices.
Wait 20 seconds seconds.
Attach the power cord.
Wait five seconds, then press the power button to turn on the computer.
If that didn't work, then reset the PRAM and NVRAM of your Mac. Follow the steps below;
Shut down your Mac
Restart and immediately hold down Command-Option-P-R keys at the same time
Hold the keys down until the computer restarts and you hear the startup sound for two or three times.
Release the keys and let the Mac bootup.
If it still not working, then get a headphone. Plug it in to your Mac and can you hear sound through it ? If so , unplug it and plug it again. Do this for 5 or 6 times and then remove it. Play something. Does it work now ?
Please let me know if that didn't work, so we can continue troubleshooting.
Do you see a red light on headphone port ?
Connect an headphone to your Mac Mini, then reset the PRAM and NVRAM again. Do you hear anything ?
Also do you have any airplay devices there ? Like airplay speakers, Apple TV etc
Resetting the PRAM and NVRAM and SMC will not hurt your Mac. In fact these are recommened steps if you experience any sounds issues.
Shut down your Mac and unplug everything. Wait 2 minutes. Connect everything back.
Turn it on and immediately hold down Command-Option-P-R keys at the same time
Hold the keys down until the computer restarts and for 5 seconds.
Now connect the headphone to your Mac and play something. Can you hear through headphones ?
Yes, we can continue later. Add a bookmark of this page or add this page to your favorites, so you can get back to me later directly. There are several causes for this problem and it may be even an hardware issue. When you reset the PRAM and NVRAM, all it did is refresh all hardware components. It would not hurt your Mac.
When you are back, we can do some advanced troubleshooting.
When you are back, please reset the SMC and PRAM one more time. Then reset the coreaudio drivers of your Mac.
To do that, open Terminal from Applications > Utilities folder. Type the following command and press return
sudo killall coreaudiod
Then restart your Mac and immediately hold down Shift key on your keyboard for 20 seconds and this will boot into safe mode. Go to System Preferences > Sound and does it recognize the output controls ? Try to play something and can you hear ?
Also unplug all external sound devices if any connected and check. If it still not working, then we can reinstall the OS X. If this is a software glitch, reinstalling the OS X will fix it.
Restart your Mac and immediately hold down Command and R keys at the same time for 15 seconds and this will boot your Mac to the Mac OS X Utilities screen. From there, click Reinstall Mac OS X. Then follow the instructions to reinstall your Mac OS X.
If that didn't work, then restart your Mac and immediately hold down Command, Option and R keys at the same time for 15 seconds and this will boot your Mac to installation screen. Follow the onscreen instructions to reinstall.
(Reinstalling the OS X won't delete any of your files. But I'd recommend to backup all your important files to an external hard drive before reinstalling the OS X)