HP notebooks are notorious for their webcams not working. Typically, the problem is a short wire issue, literally..as in the wire that connects to the webcam gets pulled out of it's socket through wear and tear (opening and closing the monitor)..it could easily disconnect the first time it's opened and closed, I know mine did. Solutions?
-Take it to a store to get repaired and make sure to let them know what you think the problem might be so they can look there first.
-Open it up yourself if you're comfortable with working on electronics. The diagram can easily be found on the hp website.
-I know it's very undesirable to get a usb webcam since you have a sleek preinstalled one, but if you exhausted all your options short of getting a new laptop you might as well stop by your favorite electronics store or purchase one online.
Hope this helps, also I had the same issue so I know how frustrating it is.
Good luck!