Is the new charger a new Apple charger or a generic one?
When you say is charging you say that because the orange light on the charger?
Try a SMC reset
Shut down your Mac.
On your built-in keyboard, press and hold all of the following keys. Your Mac might turn on.
Control on the left side of your keyboard
Option (Alt) on the left side of your keyboard
Shift on the right side of your keyboard
Keep holding all three keys for 7 seconds, then press and hold the power button as well. If your Mac is on, it will turn off as you hold the keys.
Keep holding all four keys for another 7 seconds, then release them.
Wait a few seconds, then press the power button to turn on your Mac. (Apple procedure)
Try and see if you get an image on an external monitor via HDMI port