Here are the specs for your HP Pavilion a6745f Desktop Computer. According to the specs, this model was shipped from the factory with Windows Vista Home Premium SP1 64-bit installed. When you first setup your computer, you were given many opportunities to create your own personal set of HP Recovery Discs as recommended by HP. HP Recovery Discs do not require Windows to be currently installed and working, as you boot from these discs and they return the computer to a factory like state.
I am sorry, but there is nothing that HP can do for you and your only option is to purchase HP Recovery Discs or a new copy of WIndows with a COA and valid unused product key. To purchase a set of HP Recovery Discs from HP please see "Ordering System Recovery Kit for Consumer Desktop (3 Discs)" or to purchase from third party vendor ComputerSurgeons.com see "Ordering Vista Home Premium 64 Bit (91NAv6PrA1)"
Please see KUDOS