iPhone 5 screen becomes unresponsive when plugged into a power source!

I've just recently had my iPhone 5 replaced via Apple themselves and I still have a recurring problem where when the phone is plugged into a power source, the screen fails to realise I'm even trying to use it. It becomes completely unresponsive.. Anyone else have this problem? Also it's still not picking up any 4G network when I know I should be as I work for EE and have tested my sim card in other phones and it picks it up just fine...