Take photos as digitized proof of the damaged laptop, if possible, onboard your current AA flight, in your seat showing the spills/damaged - while you are still there - see if a fellow seatmate/FT nearby might want to help you. FA might freak out but politely explain your intention to substantiate the claim for damages done.

As for soaking up & drying up, get a suitable container that cover the laptop, cover it in rice, (yes, plain uncooked rice) top to bottom & all over, battery out & power off, no attachment - let it absorb the humidity & moisture for several days. Get to a good repair shop and tell them what happened & what you've done, or at least wait a few days before starting the next bootup - the HDD should still function if it's removed as a standalone external device so that critical data can be pulled.

Good luck.