Have you tried using the "Recovery Tool" when booting?
Hold down the Command-R keys while booting during the grey screen. Full details can be found on OS X Mavericks Reinstall
That procedure should keep all your files intact. Also, you should be able to get to the Disk Utility and run some first aid and disk checking procedures there.
If that dosen't work then try downloading Ultimate Boot CD. It is a Linux based disk, but I personally have used it to diagnose issues with Macs in the past. There are a number of HDD utilities that will test out your hardware for you so you can make a determination if your hardware is good or bad. (Make sure you use the nondestructive tests)
If you hardware fails, you will need to get a new drive. You may be able to rescue the data but if you haven't done anything like this before you may want to enlist the help of a pro.
If it passes, then somehow your data got corrupt. You can typically re-intstall the OS without overwriting all your files.
Now is a good time for a drive upgrade. I would go with an SSD drive and then turn that old drive into an external USB drive for Time Machine backups or extra storage. If you go this way, you have an even better chance of recovering your files while gaining use of your computer as you work through the recovery process.
Let us know how things work as you work through the diagnostics.