If the screen is dark (no backlight, not lighting the screen), check the following;
1. Check the screen cable and screen connector for any burnt pins/melted plastic
2. Check continuity on backlight fuse (will have a little "p" or "n" on it, near the screen connector
3. Check voltage on the black diode at the top of the board, near the screen connector, above the coil.
If it is 1, replace the screen cable and LCD connector. If it is 2, replace the fuse (but check resistance to ground before turning it on, otherwise it will blow again). If it is 3, remove the backlight IC, check continuity from here to the diode, run a wire and fit new chip if no continuity or just replace chip if there is continuity.
If you think the spillage may have gone on the screen a bit, the screen PCB itself is likely toast.
Try the above. If you are not comfortable carrying out logic board repairs, I would recommend sending it somewhere at this point, since all of the above will need things to be soldered.