Is the control line properly driven it a high pull up, parts around the chip okay, well soldered, are they properly rated and having good values as given in the reference design ?? (havent seen the datasheet)
Clean input voltage ?, is the backlight circuit on the good display is under 200 ma ?
If you say your circuit work for a short time, is the driver Ic overheat ??
Good connectors contacts, I had a similar problem with our 7" Sharp displays, it was based on 3x led group on a 24vdc backlight system, when we moved the backlight fpc connector, we could see some leds (group) turned off, it gave a strange effect on the screen bottom
EDIT
OH ok i see the display specs and photos, it has eveything on its back, hdmi interface, supply input, drivers ic's etc ... nice one
Is your supply range is between 5 to 7 vdc at 1.3 amps ??
Do you use the external pwn connector ??