Yes you can borrow or download any Windows 7 retail installer for your version to clean reinstall with the Product Key on your COA sticker. The steps to get a perfect clean reinstall of Factory OEM are here:
Reinstalling Windows 7
While this is a superior cleaner install than running Factory Recovery, you may also be able to run Recovery from its partition by following these steps:
HP Backup and Recovery Manager
Then once you have recovered you can make your Recovery Disks, or another set if necessary:
HP Recov DIsks - make another set