Hello Steve Song,
it seems to be you are in trouble now,
Step 1
Replace old damaged screen and check whether functionality of device. if it works fine no need to touch logic board.
Step 2
logic board detecting by the iTunes means power and processing functionalities works fine and you need to focus on visual output, check any sign of damages in Display connector, any burn marks or can you observe any component missing on logic board?
Step 3
if you plug bad quality LCD such as back light short circuit LCD, back light driver getting damaged. i guess what you experiencing new, so you need to troubleshoot stating from coils,
* Check Display Drive instructors (Coil) 4R7 : if defective replace it
* Check the diode near 4R7 : if defective replace it
* Check the filtering cap (Down side of diode) : if defective replace it
Hope this will be help you to bring back display.
Good luck!