Here is the section from the link regarding children born on U.S. Soil:
Birth in the United StatesA child born on American soil automatically gets U.S. citizenship, unless the child is born to a foreign government official who is in the United States as a recognized diplomat. Children born in certain U.S. territories -- Puerto Rico, the Virgin Islands and Guam -- may also acquire U.S. citizenship. For details, see Title 8 of the U.S. Code, available at http://www4.law.cornell.edu/uscode/8. Anyone born with U.S. citizenship retains it for life unless he or she deliberately gives it up -- for example, by filing an oath of renunciation.
I hope that is clear enough for you, and will end this line of debate.
The mother's age only comes into play if Obama was born outside the United States. If he was born in Hawaii, he is a natural-born citizen.