The ONLY solution I have found to work personally is using a BRAND NEW, NOT SETUP iPhone and taking the home button from it. Install it in the device you'd like to have touch ID on and it will program to that device permanently.....This solution is not worth the time or money but I have had the chance to try it twice with success on an iPhone 6 and iPad Air 2.
Yes, I like to use the GEL super glue and VERY sparingly. Just a touch in the corners and you should be good. DO NOT try gluing it on the side even if it's popping out there too because it will leak into the backlight.
The most common cause of this issue with ALL Galaxy phones is the power button. Requires MINOR soldering but can be done and 99.9% of the time replacing the button fixes the issue you are experiencing.
Could be the battery definitely worth attempting replacement. However, if it's getting hot as well it could also be the PM IC (Power Management IC) or U2 charging IC both chips would be board level repairs.
I would turn it off because odds are there's still moisture in the device. Sounds like you spilled near the power button where the flex cable for your screen is, so you may have damaged one or both screen and power button. I'd dry it out completely (Damp-rid works better than rice) if you have the ability to open it do so and disconnect the battery then let it dry 100% before trying again. If it's an iPhone 4 replacing it with a 4S or 5 would be almost the same cost as fixing it.
There's a group of 5 or 6 capacitors (possibly more depending on which board you have) between the battery socket on the board and shield covering the components, check to see if any have been knocked off or loose because that is one of many reasons that will cause the behavior described....I suggest this only because you mention a battery and charge port swap and it is a common accident when doing those repairs.