Was the alt. The brushes were worn but still good, and I guess the water on it was making a contact netween 2 wires in the back, where the diodes are.
Just to make things really swell, the car refused to start, not even spinning, this morning. It was around -10 F, so I don't know if it's related. Battery might have been low. If I turned on the lights when the glow plugs were on, the relay started clattering. I'll jump-start it tonight and think better than to shut it off in low temperatures... :^)
Thanks all again.