What is the source of hard drive imminent failure warning?

Family member brought me their Compaq Presario SR513ONX to fix.  It is running Vista (fully updated) and has a Samsung SP2504C master hard drive.  It has started giving the warning "Hard disk failure is imminent.  Please back up your hard disk and have it replaced." at boot up.  Have to press F2 to continue.  Machine/system boots up ok (after F2), and seems to run ok.  I ran chkdsk; it indicated no problems (but dissappeared from the screen before I could read everything).  I ran the HP diagnotic which was preloaded on the machine; it says everything passed.  I ran ZoneAlarm's virus scan, Windows Defender, SpyBot, all no problems.  

Family member chatted with HP support.  She was told, "this is a known issue with the Seagate SATA Hard Disk Drive Utility".  She was instructed to download a patch.  She attempted to install the patch but it wouldn't install.  Support said, ok, you have a virus.  Restore the machine (back to how it was when it came out of the box with their built in restore feature), then apply the patch.  -------  The machine doesn't have a Seagate drive.  Is it really running a Seagate utility?  I think the fact that it is a Samsung drive is why the Seagate patch wouldn't install.

I did try to obtain the disk diagnostic utility from Samsung's web site for this model of hard drive.  It says, it is a DOS utility, so it must be download to a bootable 1.44 mb disk.  I don't know how to make a bootable floppy disk and even if I had one, there is no floppy drive on the machine.

Everything seems to run fine, so why it is giving me the imminent failure warning, and what do I do about it?