Well for starters leaving it sit and stew was not the best thing here. When you get your system wet with anything you need to act quickly. In this case the tea and the sugar most likely did a number on your logic board and keyboard. Sure it may appear to be OK now but over time it will be a more costly repair (if you haven't yet).
OK, Yes! you need to open up the system and fully clean it of any drink residue on the logic board and the keyboard assembly where the drink entered into the system (some versions of keyboards are riveted so you may not if you can take it off. The correct cleaner is distilled water to cut through the sugar and tea, then you need to clean the water out by using Isopropyl alcohol 85% or better. Then you need to let the alcohol dry out before you but things back together.
As to the Battery if it got wet it maybe damaged to a point you can't save it. Try clean it up if you can.
Don't forget to apply new thermo paste on the CPU & GPU chips as well.