I'm no expert and I do not know the wiring but..., I would guess that you are getting water in the cabin/around the firewall from a clogged drain. It could also be a drain tube dislodged from the condensate pan of the A/C (This happened to me in my other car. It affected the radio as well.)
You have a short that is most likely caused by water coming from above the car, as opposed to splashing up from underneath. The tough question is where?
I'd check for the obvious, water in the cabin and debris in the drain under the wipers. Other than that, a car wash followed by immediate inspection from a mechanic possibly with the dash opened up for easy inspection.
Good luck.