Go and try this first, hold the power button and the home button (large button on bottom) at the same time until the phone shows the apple logo. Then release the buttons. After a short time the phone turns its self back on. Tap the power button to see if the phone screen is back. If it is all is well.
If it does not reset, take it to an Apple Store and not Verizon since Apple will attempt to fix it first, if its broke they will replace with a brand new device on the spot.
Verizon will send you a second hand junk phone of the same make. Don't use them! Apple has a year warranty and as long as it is not physically broken or water damaged they will help you out.