Try pressing on/off, vol up, vol dn and then hold down home until the picture of charge cord pointing up saying to connect to pc and restart using iCloud. You may need to do this several times before it is recognized. This may restore back to factory new if you do not have a current backup on iCloud.
My issue is after getting to that screen it will go blank again once I unplug the charge cord possibily indicating the battery has lost connection to the processor. It will keep trying to reboot but then fails entering a never ending loop trying to start, going blank then trying to start (apple logo appears briefly each time)..