Well, the matter with liquid damage isn't the liquid itself, but how the water (and even alchol has some water in it: most liquids have) reroutes electric impulses where they're not meant to be.
So, you should let it dry. Once it's all dried, you can turn it on. Residual stains will only be ugly to see, but not that damaging. However, you cannot tell how the stains would look once they've dried out, and once they've dried out, you could simply use a really soft microfiber cloth, reopen it and rub gently.
I can tell you that denaturated alchol once left me with a faint "milky" stain on a photocopier, that went away with a gentle rub.