The problem is your lcd. The liquid crystals can freeze and won't be able to display anything. After awhile when things warm up a bit, everything will be fine.
The first couple days that temps here in Philly were below 20 F, my computer booted but I would get no video. Funny thing though - I think eventually that the lcd gets used to the cold, because this morning when I started the car, it was 1 degree F and the display was working, although reluctantly as it was very dim for a few minutes.