The Biblical definition of faith is found in
Now faith is being sure of what we hope for and certain of what we do not see. (NIV)Faith is not mere belief; it is absolute confidence. Confidence in the God we know to be there. How do we know He is there? He has shown us. He has revealed Himself to us, and He is present with us constantly in the Person of His Holy Spirit.
At about the 4-minute mark of the video, Dawkins uses the term, "faith based on reason," another misunderstanding of Christian faith. Faith is not based on reason, but of course neither is it incompatible with it. Faith is based (to which I alluded above) on revelation. Reason, given that revelation, merely confirms it.
Now, I realize that only those who have a relationship with God can understand what I'm talking about.
The man without the Spirit does not accept the things that come from the Spirit of God, for they are foolishness to him, and he cannot understand them, because they are spiritually discerned. (1 Corinthians 2:14)Someone without that relationship might claim this to be unfair or at least circular reasoning, but I'm afraid that's just the way it is.
The answer is, of course, to find that relationship yourself. It is a relationship that God has promised to all who seek it, and one that God will never deny to anyone who truly wants it.