Mac doesn't or start up
Mid 2011 Mac Mini- first became extremly slow. Then, on restart, would not get past the Apple screen. The bar seems to get to the end and stops.
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Try Safe Mode, as per > Use safe mode to isolate issues with your Mac - Apple Support
If that doesn't help, try reinstalling the macOS, as per > How to reinstall macOS from macOS Recovery - Apple Support
If you can not see the Macintosh HD or reinstall macOS on the Macintosh HD. Then there is a good chance that your Macintosh HD is failing or has failed and you need to make a service appointment with your local Apple Authorized Service Provider.