The easiest way to do this is to set up a state machine. It would look very simple.
enum GameState
{
TitleScreen = 0,
GameStarted
GameEnded
}
Something then in Game1.cs or wherever you process this button, you can put the variable in your class to save the current state of the game you are in.
GameState currentGameState = GameState.TitleScreen;
, , ,
void Draw(GameTime time)
{
if(currentGameState == GameStarted)
{
//Then handle the game drawing code here
}
}