If you have a friend with a Mac you could try connecting your system to his in Target Disk Mode this will allow your friends system to run Disk Utility on your drive to see whats wrong. I’m suspecting you may had a bad drive or the SATA cable is worn out.
If you can’t do this you could have your friend create a bootable USB thumb drive or if you have an older model a bootable FireWire drive. Then you can boot up with it to check your drive.
Another option here is to take the drive out and use a SATA to USB adapter cable like this one: Startech 2.5" SATA to USB adapter to hook up your drive to another Mac system. This will allow you to gain direct access to the drive to salvage any files to another Mac as well as test it using Disk Utility.
As you didn’t tell us if this is the a replacement drive be aware your system only supports SATA II (3.0 Gb/s) so do make sure the drive spec sheet lists this I/O speed many of the newer drives won’t run this I/O speed.
As far as the HD SATA cable it tends to wear on many of the 13” models as the aluminum uppercase has a rough surface which wears it as well as the bends around the corners. As a matter of course I replace the cable when ever I do a drive replacement just to make sure. Here’s the needed part: MacBook Unibody (A1278) Hard Drive Cable and the guide to put it in.