If it turns on and works when connected running it through a second monitor, it sounds like the logic board isn’t the part that’s damaged. When you shine a light at the internal display, do you see anything being displayed, or is it completely black? It sounds like just the display is dead, which isn’t as bad as the logic board. It might be a good idea anyway to remove the logic board and look over it to make sure there isn’t any corrosion or other liquid damage on it before you use the computer more. Do you know how bad the liquid damage originally was or what happened to it?