I had similar issues replacing broken screen on Moto G7 XT1962-1.
In my case I didn't have all the cables attached.
First it wouldn't display anything. The connection from battery was loose.
Then I found the screen connector wasn't all the way down.
Then it displayed for 30 seconds or so and then shut off.
Turns out there is a little connector wire about 1/4 to 1/3 down the right side of the motherboard that I didn't see and the wire was under the Mobo.
Once I brought it from underneath and connected it, every thing works.
Except the screen I an using is a little too small, and I am looking for a genuine Moto G7 screen, because the one I got from EBAY and another from AMAZON are both too small.
They fit, but there are gaps an the top and bottom and sides.