CErtainly sounds like either a bad battery or a power draw.  SWMBO's
Corrado has a bad diode in the alternator; however, several shops did
not correctly diagnose this.  I had to remove the alternator to get the
supercharger out and on a hunch I took it to my local FLAPS to have it
spun up on their machine and they confirmed my suspicions.  I haven't
had it rebuilt yet simply because the rest of the car isn't back together :(

nate

-18c is not that cold. Well it is fairly cold but still a good battery
with a gas engine should turn over good enough. Most auto parts stores
can hook up a test tool for the battery. Have the battery tested
somewhere pther than the dealer. Also have the charging system checked
somewhere else. You could get a volt meter to see what your running
voltage is and the voltage before trying to start. If it starts with a
jump, to me that indicates that the battery is a dud. This of course
assumes that there is no corrosion on the battery posts or where the
battery cables clamp on to the battery. But then you say that it held
a charge overnight. I would have attached my battery charger to see
what happens after a good charge. On the other hand I drive an hour
one way to work which should charge up a battery.

I never press the lock button on my car at night. It can sit in the
garage for a few days or more unlocked without any starting problems.
It sometimes sits in a cold garage. Where I live it is kind of rare to
have more than a week where it does not get above freezing. I used to
live where it was cold. Cars started all winter if they had good
batteries, good alternators, good battery cables and good alternator
wires.

http://www.batterystuff.com/tutorial_battery.html