Hi Alan,
In the interest of thoroughness, have you tried these troubleshooting techniques?
1 Plugging your Mac Mini into a different display.
2 Plugging your Mac Mini into a different outlet.
Did any lights on the Mac mini itself come on?
If so, I would suggest trying to boot into the recovery partition, or a network image.
To this with your Mac Mini, Click the Power Button while Holding down the command + R keys, Keep holding down Command + R until an image appears on the screen.
If you are able to boot into recovery, open Disk Utility and check your hard drive is mounted and recognized. It may be a good idea to try reinstalling your Mac operating system.
If no image appears, Send it in to Apple, at worst they will give you a free diagnostic of the device.
Hope this is helpful!