No light at all would seem to be a power issue so we'll try the connections first.
First, go back to the gimbal. It's possible to install the gimbal unevenly and have one side off the mounting rail. Remove the gimbal again. While it is off, if you have a rubber pencil erasure, lightly rub the contact points with the erasure to clean them. Now install the gimbal and when you are done look closely to be certain the gimbal looks evenly mounted on both sides. Now set up the H but remove the propellers. We are going to power everything up and you're probably inside the house. Even if you're outside there's no need to accidentally arm the H and send it on it's merry way when you aren't ready for it. After the H is powered up do you see any light coming from the little indicator on the camera?
With both the -16 and the H powered up, the -16 will be looking for the camera. With any luck the contact cleaning solved the problem. If not the -16 will continue looking for the camera. If the camera is not seen, go to "System Settings" on the -16 and then tap "Bind". The left side of the firmware listings that comes up is the aircraft, the right side is the camera. Does the camera side show anything? If it says "Not Connected" the system is either not seeing the camera or the camera is not receiving power. It is highly unusual for the system not to see the camera firmware unless the camera is not receiving power. Just in case tap Camera Select in the System Settings menu and select C-GO3-Pro. I doubt this would change anything but if it is seeing the camera it will at least put things in the right camera mode.
Get back to us after doing the above.