You could not test it before the new screen and even a new battery made no difference. If the Date/Time suggestion above does not work, it sounds like whatever caused the screen damage also damaged the logic board. You could have caused some Pry Damage or damaged an FPC connector during your repair. Could you somehow fully charge a battery (in another 8 ) and then install it in the device? That would help you understand if the problem is charging related or elsewhere. Charging problems are usually related to a Tristar IC being defective or PRY / FPC damage mentioned above. This can be difficult repair and unless you have the proper equipment or experience, I would recommend that you find a repair shop that can do micro-soldering repairs.
In most cases, you can solve these problems by putting the phone into recovery mode and restoring it from backup. To do that, follow these instructions: 1. Connect the iPhone's USB cable to your computer, but not your iPhone. 2. Turn your iPhone off. If the phone won't turn off in the traditional manner, just keep holding the buttons until the screen goes dark. 3. Once you've turned the device off, press the home button on the face of the device and plug in the USB cable to the device's dock connector. 4. When it turns on, keep pressing the home button until the iTunes logo appears on the screen. 5. You'll know the phone is now in recovery mode because a window in iTunes will tell you. 6. You can then start the restore process by clicking the "Restore" button in the iTunes window.