Hot coffee may have been enough to tip an already famously overheating model over the top into meltdown. If you feel up to dismantling it, start with removing your hard disk to preserve the data then strip it down to see what damage has been done. If you don't want to do that, take it to a professional.
There's residue under the keyboard, alright, all over the system board. Just because you don't see it under the keys doesn't mean it all evaporated harmlessly. With luck, the system board can be thoroughly cleaned and it might work again. Don't hold your breath; chances are your laptop will need a new board.