I assume you didn’t have to disconnect and reconnect the flex’s when adding the emf shields. Are there any marks around the connectors on the board? Does it get hot at those connectors now? Reason I ask is we just had a guy try to connect the home button and LCD connectors and was a little off. He ended up doing damage to the components right along side those connectors, and now the phone is just like you described. Good luck man
Sounds like maybe the LCD flex cable is coming loose. I’ve actually seen a guy smack the opposite side of an iPad 2 and correct a loose cable. Not sure if the 4 flex would react the same. It is a different connector altogether. You may try putting it on its right side vertically, then bump it down into your palm or lightly onto something kind of soft like rubber. Then soft reset. Hopefully your LCD isn’t going out and this helps. Otherwise you gotta open it up to investigate.