It’s very important to always disconnect the battery before disconnecting/reconnecting the screen assembly. The issue is that the LCD connector has pins that have high voltages (i.e. the backlight is ~20V) and ground in very close proximity. When you fumble around trying to line up the connector plug to the receptacle, you can short out the voltage rail and cause damage to the components in the backlight circuit. If you’re lucky, then only a backlight filter is damaged but other times, the entire circuit could be affected. Either way, this type of repair requires micro-soldering and isn’t really a DIY repair.
To test for this, plug your device into a charger or an iTunes enabled computer. Then shine a bright flashlight on the screen. If you can see a dim image, then the backlight circuit has been damaged. If you can’t see an image at all, then it may be the LCD circuit that is damaged.
You can connect the original, cracked screen to confirm this. If the original screen has the backlight on, then the replacement screen has an issue. If the original screen also doesn't show the backlight, then the backlight circuit is blown.