Sometimes these types of issues can be easily rectified by restoring the phone. You don't have to use the screen at all. Just connect it to your Mac or PC having iTunes Installed definitely. Make a Backup file through iTunes on your Mac or PC. And restore the iPhone from the iTunes. It will download the Latest iOS for the phone first to your Mac or PC. And then After the restoration. iTunes will prompt you to whether Set up a New iPhone or restore from Backup? Select the Restore from backup which you had just created before the Restoration. And Definitely you're good to go. I don't think that's a Hardware issue.