I had a similar problem, car wouldn't start, dash lights, but nothing else. Then later on, i finally got some solenoid clicking, but no starter turn over. I was concerned about the battery since i was getting a little more action when i boosted the car via a battery charger/starter (this one actually,
http://www.centurytool.net/87151_Century_15_2_100_Amp_6_12_Battery_Charger_p/87151c.htm). It wasn't much more action, but i would at least hear the starter attempting to move (but not quite turn over). I have a brand new optima yellow top battery, which was just today cited at 14.4 volts by mazda, so I do wonder if my battery was just frozen solid, i was recommended to pick up a battery blanket/warmer by mazda (which i intend on doing). I am not sure what happens when a battery freezes completely (if that's even possible with the yellow top that i have).
Also, the charger/booster that i used only pushes 100A down the line when it is in booster mode. I know that is much less than what my battery is rated at, so I am wondering if the booster simply isn't powerful enough? Finally, I did get my room mate to boost me with his running car but the results were worse than the booster. As a side note, i was a little unimpressed when his '90 integra started with minimal effort after having been sitting out in -30 for about 3 days without starting, not even plugged in. oh well...