My iPhone 4s Will only charge when power is off!!

Hi, I haven't come across with anyone with this weird problem, My iPhone 4s Cant charge whilst phone is on, and whilst its on I cant connect to computer as it wont read like the port on the phone is disabled. once the iPhone dies, that's when the phone will charge. why is this? I have got the battery changed to a new one but no luck, I try to backup via iClod as I cant connect to my computer but the battery don't last to save 32gb of data. Has anyone come across this issue? if so did you manage to rectify it? if so please can you help me with this.

Thanks in advance.

Gabriel