Retrace your steps. If it was was powering up and charging before the screen change , battery connector seems logical, since realistically that would have been something that would need to be manipulated to change the display.
It's possible that was the initial issue. But in replacing the battery connector you then introduced another variable. I would start looking at this area of the board since this nearly all the the lines from the battery connector go through this area. And this is also where the battery gas gauge data would be transmitted. make sure nothing here is bridged, or shorted.
If this information cannot be transmitted to its destination, the iPad may not be aware there is enough power in the battery to power on. Or it may be getting garbled information. I will also note, that there appears to be a missing NTC resistor where I stuck the yellow arrow. (documentation for this model seems to be a bit inconsistent, so cannot say this for sure, but the stuff I have says there should be something there). I'm not sure that this would keep it from powering on, but it might keep it from staying on.
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