Remove the battery immediately!
I'm sorry the calculator mislead you. You should never charge or turn on a device that is wet.
The Nspire is a pain to disassemble completely. There are screws underneath the plastic screen protector where the keys are. You'll need to take a blow dryer and heat up the bezel enough that the glue weakens and lifts up the screen protector. You can see the screws here: https://tiplanet.org/forum/gallery/image...
This teardown guide should help as well: Texas Instruments TI-Nspire CX Defective Button Repair
Remove the circuit board and clean it with isopropyl alcohol. Let it dry for several hours to ensure water isn't stuck under any components.
I would recommend getting a new battery. If you're lucky the calculator will turn on and start working normally. You may need to reinstall the OS but that's not super difficult. I would recommend using the N-link website for that. You can get the latest (non-jailbreakable) OS on TI's website.