Your drink has sugar & acids in it which over time will corrode things. The number of LSI markers that have turned on you is not what you need to focus on here. You need to clean what was spilled (even if its already dried).
You really need to take your logic board and the battery out so you can clean things off (see note at the bottom for more on the battery). Focus on the areas you can see wetness as well as where the LSI markers have turned red.
The best way to clean things off here is using distill water (not tap!) which will remove the sugars and dilute the acids. You will need to go over the areas a few times with a fresh cotton swab. Use a moist (not wet) cotton swab using a blotting action. If you do see any corrosion use a soft brush to scrub the area/s being careful not to pull anything off the logic board.
After you have gone over the logic board with distilled water you will need to go over it again this time you'll also use some 85% or better Isopropyl alcohol to wipe down the areas to help remove the water (acting as a dryer) and to remove any oils that may have been present in the drink. Again take care not to snag the swabs on the small components as you don't want to pull any off. You may need to use a small soft brush to scrub down any corroded areas again be careful! You can also use a can of can'ed air as well to help in drying. Don't forget to wash out the heat sink fins as well.
Batteries: Depending on how wet things got you may need to replace it. Distilled water or even Isopropyl alcohol can sort the battery so you need to be very careful on where you wipe down (get wet). I clean any surface areas that are still wet with what was spilled. I then put the whole system back together and then I turn the system back on running the battery down as far as I can. That way the amount of power is as low as I can get it before I do any deep cleaning of the battery contacts and wires (being careful not to create any shorts).
Post any pictures of areas that look bad so we can see the damage. We may have some ideas how to deal with them. - Good Luck