Edit: Frist check the Power/Data Cable or test your drive on another PC to make sure the problem is about the Disk itself!
Sometimes it is just a Corrupted MBR and you can fix your disk without formatting by rebuilding MasterBootRecord with some helps that provided here & here.
Even if you want to do the rescue by yourself using free softwares, it would be a time consuming process.
As @DavidSchwartz said, you need to take a backup first. There are some free/ bootable softwares like these.
Obviously you will need an external drive to save the Backup files and check if they are well gathered. And if not you need to change your software. If your HDD could not be accessed by those softwares and you just need a low-level backup you can use this.
If your case is a Corrupt HDD, may this software helps, although you have to pay for a bootable version or you could use the freeware if you connect your damaged HDD to another running PC. (If know what you are doing.)
After a suitable backup (or even if that fails) you even have a chance to recover your files after reformatting the drive. As many sofwares provide LOST Files/Partitions recovery.
Keep in mind that some HDD Brands offers Rescue Service like seagate.