Seems to me you have two issues, the white screen of death and the charger port. To answer your last question, yes you should be able to turn on the phone with the charger plugged into it. HOwever, you have the white screen so I am not sure you would be able to really tell if it is charging at all. The LED in the screen can be replace however I am unsure about charging issue. If you have insurance I would advise you to take the phone to your nearest Sprint repair center.
Floor Support Agent
I apologize to hear that you are having this device issue. If the new battery does not work for you, then the issue is either your charger, or the port. However if it is the port, then you will need to have the device replaced(Sprint is not able to fix this at a Services and Repair Store).
So my Katana got a white screen yesterday after i sat down with it in my front pocket and i heard a slight little pop. I took it out of my pocket and discovered it had a white screen that would not go away until i took the battery out and put it back in. I went to charge it today and it will not charge. I haven't had the chance to try out a new battery, but I will after class tonight. Im thinking it may be the actual port you plug the charger into because you should still be able to turn the phone on with it plugged into the car/wall shouldnt you? I have tried the charger with another phone, and it worked. Just looking for some feedback.