I work as a technician and workshop manager of a workshop in Stockholm, Sweden. I have about 4 years of experience and I always strive to get smarter every day. I love to help out so if you need help, let me know :-)
Basically all you can do to check if it's repairable without a motherboard repair or replacement is to connect a new screen, charging port and batteri and unplug the rest. If it still shows no picture then you have to troubleshoot it on a motherboard level.
Did you try the screens on without screws in the connector shield plate on the motherboard? Maybe it could be a long screw damage of some sort and it shorts certain circuits when a screw is in place? Does the screen work when it's not fitted into the metal body? Check the motherboard connectors for damage too.
The best would be to try to restore it with new parts. Mainly the proximity sensor causes many strange problems. My advice is that open up the phone, hook on a new charging port and a proximity sensor, run it through iTunes and then go from there.
Most likely the home button. Something similar happens on the iPad Air 2. It has a small patch with 4 points that you have to solder off and solder on to the new digitizer/LCD assembly. Otherwise the Smart Cover won't work. You could troubleshoot it by disconnecting the home button and then run the Smart Cover on the back of the iPad. If it still shuts off then it could be caused by the magnets on the side under the edge next to the LCD. But as said, most likely the home button.
My guess is that the homeflex extension cable that runs behind the shield is damaged. Even if you can't see it, it could be bent and that caused the micro rails in it to break. Try to replace it and see if it works. This might sound dumb but did you reboot it after replacement? Sometimes it forgets that it's there and will find it again upon reboot. Also, software reset might solve it too.
You probably fried the board when connecting current to it while wet. Now let's just hope that it didn't actually harm the board. If it happened recently, try to open it up and put the motherboard in an oven at about 80 degrees C. If it happened many hours or days ago, the oxidation process could already have started and then it would require a ultrasonic wash of the motherboard. So, try to dry it out as quick as possible to prevent corrosion.