Many people will argue as to where the story actually becomes interesting. What makes a story interesting is based upon a reader's engagement for the reader.
The story The Hunger Games begins to get interesting when the talk of the Games beings to arise. Readers know that something is going to happen when the text builds up the Games.
Therefore, this is the initial complication which pushes the action forward.
After this, the suspense grows even more when Prim's slip is pulled. Readers know that Katniss will not allow her sister to be a Tribute. From here on out, readers know that Katniss will do whatever she needs to do to protect her family.
It starts to get interesting when Prim's slip gets pulled out of the bowl in which they keep all the other girls slips. Katniss offers up herself instead of "sacrificing" her sister. The complications arise from here on.