Is my iPhone working when power connected and with a defect battery

is my iphone working when power connected and with a defect battery? iphone battery was empty. Connected the phone for recharge. Phone began with on/off on/off on/off (for +/- 10 minutes) recharge. Looked at the dock connector and i found corrosion on the contact surface. already replace the dock connector and for 100% in a good way. Only the phone still isn't working yet. Is it possible that my battery is defect? When i connect my phone for recharge is my phone working with a defect battery? Is it possible that the battery is defect because of he is totally empty?

Thanks in advance for your support