Q: MacMini will not "restart" or "shut down"

Shut down your Mac. Use the power button if you need to. Now start it with the Shift key held down. This will start it into Safe Mode, with all extensions turned off. Safe Mode is slow to start, so give it time, it's checking a bunch of tasks. If it works OK in Safe Mode, restart normally. If it works now, you're done.

If the problem returns after restart, you have an extension conflict. Turn off all extensions via System Preferences. To isolate which extension is at fault, turn on one extension at a time, restarting in between, until you find the bad one.