Old Earth vs. New Earth, Creationism and the Big Bang

Tonight, I sat and watched (at Bible Study) an anti-Evolution video. It was better than I expected, but sadly predictable in its fear-mongering.

The minister sitting next to me, a woman from Nigeria, kept shaking her head in disbelief every time someone said "5 million years ago..." etc etc. She firmly believes the earth is, give or take, 6000 years old. I know her motives are sincere, but it's difficult to reconcile this conviction with massive amounts of evidence to the contrary.

What do you think? Do you think the earth must be about 6000 years old, the literal Biblical date? Or something else? And while we're at it, let's toss in Creation vs. Big Bang, because that's pretty central to the subject. Your thoughts and opinions are welcome.