Well, option 3 is what's happening.
The screen is not bad, we've pretty much established that beyond doubt at this point. I suspect that the intuition of
@nlinecomputers about something being wonky at the motherboard. This is not something I can fix.
The original screen was disposed of - it went to recycling - after the first replacement that worked was installed, tested, and had been OK for several weeks. I don't keep damaged parts once it's entirely reasonable to believe they are no longer needed.
Also, I am not sending it back, as I do not have the warranty - the owner does, and she will do whatever it is that Dell wants and I will assist her in any way I can.
I can't say, honestly, that this is no longer my problem in any way, shape, or form, but it is definitely not my problem to fix. The end of my road has been reached and after a herculean good faith effort.
The issue really isn't, at least primarily, whether the fix is free of charge (though it should be, in my opinion) but that the root cause can be found in a facility that has the necessary equipment for the diagnostics needed. I don't have the equipment for doing diagnosis on a motherboard.