2 Samuel 23-24

The book of 2 Samuel ends with a note on God responding to prayers. The context makes it clear that prior to this event God was NOT accepting the prayers of his people. Chapter 24 begins with the explanation that the LORD sought to punish Israel. Yet there is no reason given for this conflict.
David led the people into sin, a path they willingly followed. So God laid out the punishment choices and David chose to fall into the hand of the living God. Through this process of punishment God revealed the future location of his ark's permanent home. (I wonder if that is a similar picture of the cross?) Once David build an altar on Araunah's threshing floor God began to accept the prayers being offered for the land.
Why would one act of worship make such and impression so as to change God's responses to the prayers of his people?
Stuart