Car won't start - battery appears fine

Looked, but didn't find a sub/r for car help. Apologies if this is the wrong spot. I've got an '02 Altima that I parked outside yesterday to do some work in the garage. In the evening it wouldn't start. Since it was hovering around 0F, I gave it a pass on the battery and decided to move it this afternoon when it's warmer. (Up to a balmy 24F right now). Still won't start. I backed the other car out to try and jump it, but it's still dead.

Symptoms: When I first go to start it, it'll turn over barely, sputter for a few seconds, then immediately die. Subsequent attempts will won't turn over. Same effect after trying to jump it. Turned over for half a second, then sputtered and died. It did t his the last time it was really cold and I had the battery tested. Supposedly its fine.

What could cause it to not start in cold weather when the battery's okay? It can't be the starter, since it starts every other time and even turns over right now, right?