Its is most likely the battery, given the temperature. It could also be the starter, but like I said because of the extreme temps it is most likely the battery. When it was clicking, it was because the battery has enough juice to engage the starter solenoid, but not enough to turn the starter motor and start the engine. As for the no clicks and sparks when she re-installed it, she probably put the cables on backwards. I would have her go pick up a battery (if someone is nice enough to give her a ride) and hopefully it will start up right away! As for condensation in the line and frozen gas lines, this is always a possibility in winter months. However, this would have no effect on the motor actually cranking over. It is also unlikely to be the distributor because the motor would still crank over if the distributor was bad. I should note though that the bearing inside the distributor is known to lock up. I'm not sure if this would prevent the motor from cranking over or not. Someone else might be able to chime in on this one. As I said, given the circumstances, the battery is the likely culprit. BTW, if she still has a few more years left at this school (in harsh winter climates) I'd advise her to get a good battery, not a cheap one!