Turn on the computer, give it enough time to boot up, then use the following keyboard shortcut:

Control-Option-Command-Eject

That should cause the Mac Mini to shut itself down again. If it shuts down of its own accord, it probably at least managed to boot OS X successfully; if it doesn't, then it's probably stuck somewhere.


Another option (if you have some way of hearing the sound output) is to simply use the volume controls built in to the F-keys, and listen for the "popping" sound used to indicate the new volume.