First thing try to restart it by pressing the home and power buttons and see if the problem is solved. If not:Try to do a software using itunes, first thing turn off your phone (if it doesn't respond to touch, press the power and home buttons together and when the screen goes black, connect the usb charger to the computer then to your phone and when you see the apple logo, press the home button until you get the itunes cable (Recovery mode) the itunes will open automatically if it's already installed or maybe you need to open it manually then press the restore and let the phone restore itself. If it still have the same problem, take it to a specialist or if you know how to open your iPhone you can try to disconnect the screen cables and return them.
Try to connect it to the computer and when U see the Apple logo, press home and power buttons together to restart ur phone , then try to open itunes and do like update or restore. If not:maybe it's the same problem that happened to me 2 weeks ago, my iPhone 5 was showing the apple logo then the itunes cable (like recovery mode) I tried alot things but it was stuck to the itunes cable then I just replaced the battery and it turned on with no problem.
Try to restart the phone by pressing the home and power buttons together for couple second, if U just heard a vibration sound and no screen I suggest U to open the phone and check the connection between the screen and the motherboard because maybe one of the cable may be broken or just not connected
Check the imei in settings or call *#06# check if it's the same as on your iPhone box Maybe they tried to replace your motherboard with another one which is blacklisted or something like that or you bought the phone from a person who stole it from someone else