2014 Cruze Diesel, 2007 Cobalt, 1981 Camaro Z28, 2017 Volt
Oh well that explains it quite well! I was doing the exact same thing - trying to use my jack under the front subframe (I was using one of those trolley jacks and a piece of wood - the wood slipped because the subframe is rounded), and I had a jackstand at the ready to go underneath the subframe and it just happened to be under the radiator.The same thing that happened to you.
Last year I tried jacking the front of the car up the front of the subframe. The jack rolled and the car slipped. I didn't think it cause any damage but it turns out it did.
I've actually never owned a car without functional A/C so, not having A/C would suck June - August.