You can read about the big bang on several of the catastrophism links from my post 144 on this thread. It's basically a fairytale based on misinterpretation of redshift phenomena but you don't need to be a physicist to comprehend the absurdity of it. Having all the mass in the universe collapsed to a point would be the mother of all black holes; nothing could "big-bang" its way out of something like that.
As to carbon dating, it absolutely depends on the idea of the ratios of carbon types in the atmosphere and the soil having always been what they are now, which is absurd. Even items from the beginning of the industrial revolution in England often date as if from the time of Attilla the hun because of all the soot in the air in England at that time.