1. Go into Spotlight from the top of your Mac Mini on the menu bar.
2. And search for "CDs & DVDs" (It's also in the System Preferences)
Click on it and a small CDs & DVDs window will pop up with options of what happens when you insert a disk into the drive
3. By then, try inserting a disk in (while that window is open. This kinda wakes up your drive to accept the disk). It should accept it.
4. If nothing happens, then manually open the program that should be opening when you insert the disk or go to Finder (Eg. if it's an audio disk, then open iTunes)
5. If opening the program still does not activate the drive to start spinning the disk, then close the programs and windows you opened, and repeat step 1-4 and the disk should be spinning and automatically opening the proper program.
Or go into Terminal app and type in: drutil ejec
The drutil ejec tip is credited to Dan8954
Hope that helps!