The most important thing to keep in mind is that liquid can short out the computer and fry the board, so DO NOT turn it on until you're sure it is 100% dry. This can take a couple days. Also remove the battery, because the battery provides power to the laptop and can also cause problems.
Diet Coke is a corrosive substance, so the longer it stays in the computer, the more damage it can potentially do. If you're comfortable opening the machine up, follow the appropriate iFixit guide for your computer and clean up all signs of the liquid spill with 90% rubbing alcohol and q-tips.
It's possible your logic board has been fried, although it's also possible it will work again once it has completely dried, or after the liquid has been cleaned out as I described. It's also possible that just the DC-in board has been fried (and not the logic board), in which case you can just replace that part, which is a relatively minor expense ($50-$100 for the DC-in board, plus the procedure to swap it out). When you connect the AC adapter to the laptop, what color is the light on the plug, or is there no light? If it is green/amber and behaves normally, that may indicate the logic board has been affected, and if there is no light, that would tend to point toward the DC-in board.