I would also suspect the backlight circuit (just shine a torch on the display and check if you can see the lcd image) . As already stated, when applying heat to a board where the components are so close together, the chance of disturbing an unwanted component is extremely high and there is an equally high chance of effecting the backlight circuit. When soldering Smd parts, I always use captan tape surrounding the component in question to reduce the chance of heat spreading to unwanted areas.
This sounds like textbook back light failure. The phone will power up and appear to work normally except the screen. When shining a light on the screen, you can see the images but very dim. This can happen if the battery is still connected when removing/installing the FPC Flex connectors causing a short or arcing at the terminal blowing the backlight circuit. This happens alot with the Ipad mini, I've seen very few phones with it but it does happen to the 6. The usual fix would be firstly trying a different screen (in case it's the backlight itself at fault) or failing that, it would mean replacing the backlight IC (U1502), filters, coils and diodes. Not expensive but you will need surface mount soldering equipment and experience because it's a difficult repair!.