Sounds to me like the new battery isn't calibrated to the device. What I mean is that the battery may think it is 100% full, but because the phone hasn't gathered data such as the fully charged and fully drained point it doesn't know where it is. It could read 100% but may actually be fully discharged.
Turn it off and charge it overnight. Unplug it and plug it back in every once in a while during the process to make sure that the charger pumps a little bit more juice in each time. See if you can do a factory reset too, only after you try to charge it overnight though.