Why won't my phone stay one off of the changer?

I am guessing your problem is related to the battery. Only turning on when connected to a charger can be a sign of a dead battery. But If pressing on the screen can keep the phone on for awhile when it's disconnected from the charger, then the battery's connection to the logic board may be loose. Try reseating the battery's connection to the logic board to see if this will fix the problem. If not then a new battery should solve the problem. You may also check for other loose connections to see if that could be causing your Wi-Fi problem. Hope this helps.