I have a similar problem. For the lights, I think it’s the cable between the LEDs and the board that is very fragile. I bent it under the board so the cable would be a bit smoother. Still, I don’t understand the loss of connectivity once every couple of minutes.
Done. I took my time and the most difficult chapter was to put on the new screen and get the cables through the hole without crushing them behind the screen. Oh and find a good screen, too : most parts are good enough for the price, but I wonder where we could get actual retina apple display. Apple does not support iPhone 4 anymore, they should release their stock.