Well CRAP, should have left it alone.
Apparently the controller just got wet.
It's mounted behind the radiator support so it doesn't normally get wet even in heavy rain.
I pulled it and brought in in the house, submerged the sensor in a pan of water on the stove and made it cycle on and off a few times while watching it with a thermometer and a ohm meter and it acted completely normal, so I guess everything is fine.
It's all back together now.
