Sounds like it's too late, because the _first thing you should have done_ without exception would be to not supply power to it. You did and probably shorted it.
You can purchase a kit to clean electronics. Mostly you just need it for the brush and a micro cloth is good too. You should clean it with distilled water. You don't want to use tap because that contains minerals that will most likely leave residue. You would want to disassemble and thoroughly clean the unit, but really it depends where exactly the soda was spilled. I don't know offhand what effect that has if it contacted the screen, and I imagine it can't be good for speakers. But everything pertaining to the buttons, the circuit board, etc. would be salvageable.
But again, that was provided you hadn't supplied power to it. You can try it anyway, but it's likely totalled. I've seen exactly what you describe in other gadgets that were submerged in some type of liquid, either while powered or after the fact. It's to be expected that current would make it to something like an LED but fail to boot.