There is no cost associated with Hero Blast. When Hero Blast is activated, 2 targets are chosen, 1 is a monster on the opponent's field (optional) and the other is a Hero in the player's graveyard. The card resolves by destroying the targeted monster (if there was one and if it still exists), and then bringing the Hero monster from the graveyard to the hand.
When Hero Blast is activated, you can chain D.D. Crow and banish the targeted Hero monster in the graveyard. Since it is a chain, Crow resolves before Hero Blast (chains resolve backward), and the targeted Hero monster will no longer be in the graveyard so Hero Blast will not receive that part of the effect (although it will still destroy a monster on the field if one was selected).