My iPad mini just went blank. 6 months old. No response at all. Now what?

A reset may help. Tap and hold the Home button and the On/Off buttons for approximately 10-15 seconds, until the Apple logo reappears. When the logo appears, release both buttons.

No content is affected by this procedure.

Has it been charged recently? Connect it to the external charger and verify that the unit is being charged. If it's dead, let it charge for a few hours.