I contacted a 2nd Apple Repair Centre via email. Told them of my iPhone problem. That a connector had been repaired. Worked for a while. Then the screen stopped working again. Their reply:
"Since you have done an iOS reinstall, then next step is to replace the screen temporarily. We will also check the connector to see if anything is loose. It could very well be just a defective screen which needs to be replaced. If there is something wrong with the cable connector, then reconnecting it may not do the job as the problem can come back again, but we will open it up and know more once we see it.
Screen replacement, parts, labour to install and lifetime warranty for any defects: $150
The repair takes about one hour. If it is a problem with the motherboard, we can take a look at that as well."
If it's only a screen replace, I will do that. If it's a motherboard problem, that's too costly to do. Because I have to mail it to them, is there anything else I should ask for?