I guess that you dont have too much to lose in playing around to see if you can get it working again...
I would probably try and dry it out first for a few days.... try the rice idea and then after 2-3 days try again...
if this does not work... try dunking it in freshwater for a few days (make sure to remove battery & memory card
).... after this, back in the rice to dry off.... you may need to refresh the rice as it moistens.
If that does not work you can try and break the jigsaw apart and clean the boards in fresh water... I have never opened a DSLR so am unsure how easy/complicated this may be... I do expect however if you get this far you really dont have much to lose if you break something.