iPhone 5S Broken Screen / Not Working

I have had my iPhone 5S for about 1 1/2 years. I dropped it a few times and had the screen replaced. Recently it cracked again but was working fine. About two nights ago it dropped on the ground and it cracked more and the phone seemed frozen on the lockscreen although distorted, i pressed the Power + Home buttons and the screen went black. Since then it wont turn on, respond to vibrate/Touch ID and the screen stays black. I plugged it into iTunes and it appeared as charging and it made the vibrate sound when i plugged my phone in, still no responding from moving the vibrate button though. Is it just the screen that has to be replaced or has the phone been damaged in the process?

Any help/ideas/remedies much appreciated!

Thank you.