I have an iPhone 5 that's really giving me a headache.

At first it started up but the screen wouldn't come on = it synched with iTunes and vibrate on/off worked, but replacing the screen didn't work. There's no visible liquid damage but I suspect it might have been a victim of a static discharge working environment.

I've had the backlight coil replaced(the likely suspect) on the logic board but now it's stuck in DFU-mode and won't go any further than "Waiting for iPhone" in iTunes and an Apple logo on the screen with an empty progress bar below. Now I'm thinking the backlight coil might not have been faulty after all.

What are the likely suspects in this case? I'm tried to restore with several dock connectors/flex cables and USB cables but nothing seems to work.

Could it be the flash memory? Any good ideas for a fix that doesn't require completely replacing the flash chip?