Black screen - iPhone 5c

My daughter's iphone (5c - not sure of the version) screen went black one morning. We could still feel the vibration when we switched from volume to mute on the side button. Tried to force a restart by holding down Home button and the top button. Now we get nothing. I was told by Apple to do a force restart (with reset to factory settings). They told me to open itunes on the computer, plug in the phone and hold the Home button and the top till the apple appeared on the screen. I held it for a minute, with no apple. Itunes recognizes that my daughter's phone is there. What should i do?