This happened to ours, minus the crack. It was 3 years old and just.... nothing.
We tried a hard re-set (I googled for directions). Then I called apple tech service and they walked me through a few ideas. Then we tried a few other things that we googled (having to do with trying to sync it to our computer/itunes). Nothing. Cost to repair was too high (as much as a new mini) so we got a new mini.
A few months later, H gave it one last-ditch effort before we dropped it off at an e-waste event. Boom, plugged it in, it turned on, and has been chugging along for the past 6 months.
So now we have 2 ipads. Oops.