Remove the bottom cover, disconnect the battery, disconnect and check the backlight connector (to the right of the left fan, at the top of the board). Since this is at the edge of the board, it is very easy for it to get liquid damaged and damage the connector on the board. If there is any corrosion, clean it with isopropyl. If not, it could be an issue with the part (very unlikely for it to not work at all, unless opened and damaged before) or it could be an issue with the backlight IC for the keyboard backlight. If the connector is burnt, you will have to solder a new one.
Before all this, try an SMC and PRAM reset. Also, put your hand over the camera and try increasing the backlight using the keyboard.