The blue is corrosion! What was spilled into the system?
You'll need to disconnect the battery and then using distilled water (not tap!), wipe the areas down removing as much as you can with Q-Tips making sure not to snag anything. In this case you'll likely need an acid to clean off the copper oxide. Use white vinegar and then go over the area a few times with the distilled water to neutralize the acid. Once you have gone over the logic board (both sides) wipe down the areas again with a good quality of isopropyl alcohol (reagent being the best). This will remove any oil residues and help in drying the water out. Let the board fully dry (give it a good day sitting in a sunny window).
If you still have problems with the clean up post some pictures of the areas you are having problems or questions. Good Luck!