Youre definitely on the right track. It's probably less that the battery is dead (though the previous one maybe have been) and more that either there is an electrical short somewhere dumping all the energy from the battery into ground. Or your phone just can't charge a dead battery.
Based on the heat I am inclined toward the former. If you're lucky it's a bad part and not a bad board component. If it was getting hot around the camera area I would pop open the phone again. Disconnect the battery and then disconnect the front facing camera from the board (it's [guide|55940|the lower-most connector in the stack|stepid=121180|new_window=true] coming off the display) And the rear facing camera. See if you get power then. If so, you can narrow it down between the two.