Sometimes new batteries are under the operating voltage meaning that it may not allow the phone to display a charging icon when you plug the phone in with the new battery to charge it.
Once the battery voltage is high enough it will start to display a charging icon on the screen to indicate that the battery is charging.
Depending on how flat it is it may either take a long time or if the battery is faulty the battery voltage will not go up.
You can check the battery voltage by using a digital multimeter and using the probes on the battery terminals (on the battery).