I can't say I've ever seen the socket go bad. But, I have had to disconnect, clean with contact cleaner and reconnect before. You have to be really specific with your testing. Any pushing you are doing is flexing the entire board and screen. This is either the cable or screen and based on your comments Id say the screen.
Remove the bezel. Place your fingers at the bottom center of the laptop screen. Then, gently slide your fingers or a thin plastic spudger between the bezel and the screen. Pull the bezel with your fingers and it should snap loose. If it does not, try pulling it gently in different directions until it comes loose. OSusu1.