Remove the bottom cover, check to see if there is any visible liquid damage. If there is not, remove the battery, disconnect the keyboard (plugged into the trackpad), reconnect the battery and then plug in the charger.
The MacBook will hopefully turn on by itself. Leave it running, and see if you experience the same issue as before. If you have an external keyboard, you can reassemble the MacBook (leaving the keyboard disconnected) and use it, to see if it is fine.
If it is working fine, the issue is with the keyboard itself, sometimes the power button will shut down the Mac if it has suffered minor liquid damage.