Thank you for the ready response with the information I requested.
At 2 years, the camera is out of warranty, first.
It is good to know that the camera has been cared for, but being splashed with water could have affected it.
The new battery put into it, was it charged up thoroughly? a rechargeable battery that is new, should be given an initial 6 hours on the charger, before first use, owing to its having sat of a shelf unused for a while.
Try removing the batteries, and leaving the camera on a (dry, non-humid, non-dusty) shelf for overnight. Then put the batteries back in and try the camera again.
Then try cleaning the terminals in the battery compartment, after removing the batteries, first by rubbing off with a fresh pencil eraser, then by wiping the terminals off with cotton swabs moistened in rubbing alcohol, then letting them dry off for 5+ minutes with the battery compartment door open, then try turning the camera On again.
Let me know the results of those things-to-try, if you would, by and by when they are done, please.