can you see anything at all using the cracked screen? if it is partially usable with the cracked LCD that will help determine its an LCD problem.
Now there are three possibilities with any display issues where the picture is not coming up properly: the LCD, the display cable, or the logic board.
Generally an LCD issue is going to have the line issue or a portion of the screen is blank while the other portion works fine.
If the display cable is damaged, a good test is tilting the display back and forth and see if the problem gets better or worse. If it does, there is most likely some cable damage somewhere.
For the logic board, it helps rule it out like you did using an external display, but there is still a separate output to the display on the logic board which can go bad.
For an LCD issue, the only test is trying a new LCD. As i mentioned earlier, you can try the cracked LCD and see if the picture shows up where the screen isn't cracked as bad. If it doesn't, it may be something in addition to the screen that needs to be replaced.
Now, I don't recommend doing this as it can be dangerous, but you can try pushing down on the connection on the logic board where the display cable is connected and see if it starts working. This can narrow it down to a problem with that end of the cable or a problem with that connector on the logic board.
Generally at this point, I would probably take it somewhere to get diagnosed since it may require trying out several parts to find the problem.