Screen keeps shutting off

Hello, it looks like you either have a malware (very rare) or a corrupted ROM (firmware). Now, you can try to hard reset your phone. Even though I have no information if the phone is rooted or not, try the next steps:
1. Turn off the phone, in your case, it can't stay on, so let's say this step is already cover.
2. Press and hold at the same time: Camera key, volume up and power key, and let them go ONLY 2 or 3 seconds after the Android logo is display.
3. Scroll down to Wipe Data/factory and highlighted, tap home to choose, scroll down to yes and tap home to select.
4, Go back to the main recovery page and do the same thing but with Wipe Cache as you did with step 3.
5. Once that is down, go back to the recovery main page, scroll up to Reboot, and tap home to select.
This process is to clean your phone and leave it as brand new, as when your first bought, if it wasn't bought second hands or used. In most case it does fix the problem with the firmware and fixing the permissions need in order to function properly. If after this you still have a boot problem, then your device needs to be flash with a new firmware.