JoyNampm,
That's correct. If it doesn't start after thawing, than your problem is obviously elsewhere. Mechanics will tell you your car needs 2 basic things to start; fuel and spark. Do you have a way of charging the battery or jumping the car's battery from another car? Your car's battery may be getting pretty weak from all the attempts to start it along with the cold weather.
By the way, it was around 0 here in the Chicago area last night so I wouldn't expect a warmup any time soon.
Mike