The message "disk boot failure" is only found in the ROM BIOS and is displayed when the boot code in the partition table is corrupt (Head 0, Cylinder 0, Sector 0). Errors in the MBR (Head 1, Cylinder 0, Sector 0) will result in "Non System Disk" errors.
If the drive has not spun up and reported as ready to the BIOS during POST, most newer BIOS's will report that no bootable device was found; a different error altogether.
If it were an older system, I would be suspicious of bad capacitors; but, most reputable manufacturers got burned badly by that one in 2000-2002 and are more careful, these days. The same is true of subspec power supplies (though the burn was in the late 1990's) and, unless you have added something like a $600 gaming video adapter, I doubt it to be the cause, either.
What's left is the hard disk drive itself and first, I'll contradict the HP support. Please (!!!!), everybody, enable the SMART reporting in your BIOS. I have been doing data recoveries since 1979 and regularly find that the SMART data in the drive indicated impending doom months before the catastrophe. What bugs me is that Microsoft hasn't built it into Windows. Wouldn't any of you who had a drive fail love to have had a message pop up saying "Your Hard Disk Drive is Failing"? Windows has supported it since Win95!
My suggestion is that you go get http://www.hdtune.com It is a freeware utility to let you inspect the SMART attributes of the drive and to perform a low level error scan. From the way you describe things, I'll bet the only shows a decided pause in the first block during the error scan; but, I'll bet it is there nevertheless.
If you have not already done so, make the recovery CD's now so you can replace the hard disk drive. They don't come with new computers, you have to make them. Back up anything you have done (spreadsheets, documents, pictures, etc.) while you are at it.
After you have done those things, you ought to be able to get a new drive from HP by being cranky about it or, at least when it fails completely, you'll be ready.
As a final note; there is the chance that Spinrite might fix the problem if it is due to a marginal write on the media. Reading the partition table and writing it back may actually fix it; BUT, if it is due to an actual defect in the drive, it will never boot again afterwards so, please, make the recovery CD's and backups before you try it.