Chosen Solution
I have a mid-2012 13’ Unibody MacBook Pro. After a spill, the power button does not work if the battery is attached. I was following the directions to power on from the “power pads” when I discovered that if the battery is not attached, but the computer is connected to AC power the button works just fine. Short term my solution has been to just never shutdown the MacBook, but I would like to try and fix the problem. However, I am not sure if there is a way to test if the problem is caused by the battery (which is easy to replace), the keyboard (which would mean replacing the upper case), or the logic board (in which case I would probably just live with the status quo).
There are two power circuits on the MBP logic board. One for the power provided by the charger and one for the power coming from the battery. To troubleshoot your system I would begin by using a known working battery cause maybe the battery is the culprit. But before doing this make sure the logic board is cleaned from the spill and inspect it carefully (both sides), check for corroded area, black short-circuit spots, anything abnormal.
See this question and tell me know if it answers you: Half of Keyboard not working after water spill