1993 Ford Crown Victoria car will not start

My daughter has a 1993 Crown Vic LX with 175k on it. She drove it to work yesterday and it ran fine. I drove it the day before and it started right up and ran with no problems. When she was ready to leave work last night the car would not start. When I turn the key I get nothing. The dash lights up and the check engine light, battery indicator and airbag indictor are on. The interior lights and headlights work. The heater runs and The radio works but I'm getting nothing from the ignition, not even a click from the starter. The battery has plenty of juice and the battery level registers on the dash. It's been around 0 to 4 degrees at night the past few days and in the 20 degree range during the day. So figuring that the old battery may not have enough CCA's I put a new battery in it with 600 CCA's and it still did the same thing. Nothing. My daughter said that it started up as usual on the first crank and drove fine on her way to work. Any ideas?