Weird problems with the LCD. Very strange.

OK. I have this iPad 2 GSM that the LCD is glitchy. I let it die all the way and try to turn it on, the screen lights up like you would expect and tells you the battery is dead. So, I plug it in and let it charge for a day. Now press the power or home and the screen's backlight does not light up. You can see what is on the screen with flashlight, but no backlight. Let it sit until the battery dies and you are back to the dead battery notice with the backlight actually turning on. I have replaced the touch screen, the LCD, and the WiFi antenna. I have two different LCDs that do the same thing no matter what.

What cold be causing this strange behavior?