What, exactly, makes the Capitol so powerful?

The Capitol maintains strict control of its surrounding districts in The Hunger Games through fear. One way in which the Capitol ensures and maintains fear is through the Reaping process. Since there is often a shortage of food in the districts, there is a fear of starvation. Eligible participants in the Reaping have the choice to receive a "year's supply of grain and oil for one person" in exchange for having additional entries of their names in the drawing. Katniss shares that Gale will have his name entered forty-two times.
Each year before the Reaping, the mayor of the district must read the same story detailing information about the "Dark Days." This is the name given to represent when the districts rebelled against the Capitol. The Hunger Games are instituted as a result of these uprisings. Katniss believes that "Taking the kids from our districts, forcing them to kill one another while we watch" is the Capitol's way of keeping the districts from rebelling again. Those in the districts are fearful of what may happen if they show any disapproval of the Capitol's control.
At the end of the games, Katniss ensures that she and Peeta can both win when she gives him the idea of eating the berries. As the last two survivors, Katniss and Peeta will deny the Capitol a victor if they eat the berries and die. This turns out to be a dangerous move for Katniss. She discovers that President Snow is unhappy because she determines the end of the games by making the threat with the berries. This shows a small flaw in the control of the Capitol. Katniss learns that she must pretend to have made her decision through her love of Peeta and not out of spite for the Capitol. Evidence of this is provided when she says, "the Hunger Games are their weapon and you are not supposed to be able to defeat it." The Capitol, in an effort to maintain control through fear, must oppress any open sign of weakness in their system and rebellion in the districts.