When your hard drive is continuously spinning it could be caused by a couple of things. The first and easiest thing to do is to run a disk defragmenter on the drive (not applicable for SSD drives). When a hard drive becomes fragmented it has to search the disk in several different places that are spread out to get the information rather than in just one contiguous section. You should check it about once a month to see if it needs to be run.
Another reason a hard drive will be constantly working is because you do not have enough RAM in your system and the computer has to go to the hard drive for memory to make up for it.
I would also check your startup items to make sure you don't have any unnecessary programs starting with your computer using up your resources and running in the background.
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.