I have similar problem and I tried replacing power supply and using the washer trick. Neither worked. Sony will fix out of warranty for $99+taxes or I can go to the local repair shop which they quoted $60+ with diag. I might just send it to Sony.
I had GTAV that did something like this until it wouldn't play at all. When they burn the discs during manufacturing some come out bad like with electronics. So I returned it to Gamestop and got a replacement. Solved the problem. You can either buy new games or contact Sony/Publisher and see if they will replace.
You can get a screen from Ebay or do a Google search. But the cost is half the cost of the tablet. So its around $200+