If the drive failed, it's highly unlikely anyone except the NSA would be able to get information off of it. Certainly HP isn't going to bother. Most likely they will send you a new drive, and recycle the old one. Or even if they refurbish it, they'll probably need to low-level format the platters, wiping out the info permanently.
I personally think too many hard drives are needlessly destroyed because of worry the data will fall into the wrong hands. Think of it this way. If you found an old drive in a dumpster, would you bother sending it to the NSA to see what's on it? Most people will just see if the drive works, and then proceed to format it and use it. A few passes with any commercial drive erasing software should be sufficient if you wish to dispose of or resell an old hard drive. If the drive doesn't work at all, chances are good the data on it is safe from prying eyes. It's just not worth it to try and get data off a drive unless you're certain that the drive contains valuable data. Imagine spending thousands of dollars only to find a drive has family photos?
Incidentally, I'm even hearing of people destroying SSDs because they fear the data will fall into the wrong hands. Once you secure erase an SSD, the data is toast, as in cannot be recovered by any means by anyone, including the NSA.