MBP not restarting after shut down - have to disconnect the battery

For the past 3 years or so my wife and kids has been using my old MBP after I got a newer one.  It’s pretty much left on 24/7 only restarting for software updates etc. very rarely shutdown. It’s connected to an external keyboard and screen so the builtin keyboard is never used.

For a few weeks now the mouse has increasing been displaying the control menu options with a normal left button press. I’ve tried several keyboards but it’s like the ‘ctrl’ button is permanently down and all left clicks are behaving like right clicks. When I checked the laptop keyboard, I noticed the keys in the bottom left section were sticking so there must have been some liquid damage causing the issue. No one has owned up to it :)

I decided to shutdown, disconnect everything so I can remove a few keys to see how bad the damage was and that was it - couldn’t restart. It was like the MB was dead. I was able to get it restarted but it would only boot in safe mode even after resetting the smc and pram.

A few hours later - I can now get the MB to boot normally with the builtin keyboard disconnected and using an external one. Everything works as expected including the mouse but if I shut down, I cannot use the power button to restart. The only way to restart is to disconnect and reconnect the battery and it restarts when the power cable is connected.  Restarts are ok from the apple menu.

I don’t know if the keyboard is connected to the power button so before I replace the keyboard, I wanted to see if any one think there could be other damage that would explain the power button not rebooting the MB after a shutdown.