A corrupted hard drive could definitely cause issues like this. Since you are unable to boot even to a recovery disk, and Dell Diagnostics is giving you warnings, that indicates that it is more than just that particular Vista installation.
I would recommend using a hard drive analysis tool to check the drive for errors. Most hard drive manufacturers have bootable disk images you can download to boot off of and check the hard drive without having to boot into Windows. If files critical to the boot-up process have been damaged, that could prevent Windows from booting successfully.
If you determine that the hard drive is indeed corrupted, you will need to buy a replacement. Since the Dell Diagnostics indicate that there is a hard drive error, this will most likely be the case. If you want to recover the data from the hard drive, you will need to find software that can help you with that.
If you can manage to boot into a Windows Recovery Console, you could use
chkdsk to fix the disk (to the extent possible), allowing you to copy off files. Failing that, see if a Linux Live CD can successfully boot - I haven't personally used it, but Ubuntu Rescue Edition may do the trick. Otherwise, you may need to turn to something else. I use SpinRite for this, which is fantastic software but not free. There probably exists a free alternative; you would have to do some googling.
If you need help determining what type of hard drive to get to replace this one with, let us know.