Why won't my iPhone let me unlock it?
The screen on my iPhone goes black every time I type in the password. I can also see my notification but not respond to them. How do I fix this?
iPhone 6, iOS 7.1.2
First, reset the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back again. You will not lose any data by resetting, but it can cure some glitches.
If this does not work, and to make sure that this is not software related, set it back to factory settings, without using any backup data afterwards. Set up the rest of the personal settings manually and test the phone.
If the phone works as expected, restore from the latest backup. If the problem comes back, the backup data contained corrupt data, causing your issues.
If it still does not work, this is a hardware issue and the phone has to be serviced by Apple or an Authorized Apple Service Provider:
Use iTunes to restore your iOS device to factory settings - Apple Support