The coils look like they were damaged when you removed the shield. I'm a little concerned about the second and third one from the top. On the third and fourth pictures, I notice some solder balls between the CPU and the components. This could be related to the overheating but more likely you applied too much heat when removing the shield. What did you use to desolder the shield?
As far as your original problem (no screen image), it sounds like it may be a backlight circuit issue. You need to check the ferrite bead that filters (Fl2024) the anode line (PP_LCM_BL_ANODE) for the backlight. Then work your way upstream towards the diode (D1501) and filter (L1503). Hopefully you have the schematics, otherwise, search for it on Google to help you locate the components.
Get back to me by commenting on my answer and let me know what you find on the backlight circuit and please confirm if what I see are solder balls (that would be bad news).