What is the conflict that is driving the protagonist, Katniss, to act in The Hunger Games?
The conflict that drives Katniss to act changes as the story progresses. I hesitate to try and name a single conflict that is able to encompass all of her actions.
I think an ever present conflict for Katniss is an external conflict. At times it is man vs. man, and at other times it is man vs. nature. Her conflict is even man vs. society at other times. All of those conflict types though are squarely focused on one thing though. Katniss's survival.
When the book opens up, Katniss's conflict is with being able to obtain enough food for herself and her family. It's a basic conflict against starvation and malnutrition. In the arena, the conflict is still focused on her survival. She still must obtain food and water for herself, but now she has to worry about other teenagers trying to kill her. Keeping Peeta alive is a part of that conflict. As the "game" progresses, the creators increase the difficulty by introducing additional dangers into the arena. Katniss's central goal of surviving is still number one though.
Cinna is the character that helps Katniss understand that her survival is also dependent on the people of the Capitol. Once Katniss understands this, her actions change as well. She learns to play to the crowd, which in turn helps her secure sponsors. Sponsors help keep her alive.
I can't make the claim that Katniss does everything for her own survival though. Prim is the person that was chosen for The Hunger Games. Katniss could have guaranteed her own survival for one more year, if she had let Prim go to the Games. Protecting Prim motivated Katniss to volunteer as tribute. This is a case where Katniss's internal conflict motivated her to do something that put herself at great risk.