Depending on the brand you may be able to find a diagnostic tool to test your drive. Most major manufacturers offer tools to test with. Some are designed to work from within Windows and others can be run off of boot disks so you will have to see what you can find online.
You can also take out the drive and put it in an external hard drive caddy or as a secondary drive in another computer and see if you can access it that way. If so you can copy your files off the drive and then think about replacing the drive or at least put a different hard drive in your computer and see if you can get that one to work with your computer.
Another test method is to boot your computer with a Linux boot disk and run a copy of Linux off the CD and see if you can access your files that way. You can use a version of Linux such as Ubuntu or Knoppix to do this type of test. Doing this will also allow you to copy files to an external drive or USB flash drive to make a backup of your files.