It sounds like your disk is very sick or dead. Let’s hope it is the former. I would do nothing to it (including booting it) until you get a new drive. Anything you do may make it worse.
Back to health and emergency data recovery:
You can install a new drive yourself, format it and install OS X on it. You can then put the old drive in an external enclosure, try to mount it, and then use the Finder to drag all the files you can onto the new system drive. Of course if it is to far gone then that won’t do any good but you won’t know until you try. Since it booted in Recovery Mode that says at least part of the disk is OK.
I recommend the following equipment and procedures:
You might as well purchase a new super-fast hybrid drive for under $100 than has an 8 GB SSD cache that makes the data fly. Google “Seagate 1 TB hybrid SSHD”.
You will need special screwdrivers to open the Mac and deal with the screws on the hard drive.
$5 Toolkit: http://eshop.macsales.com/item/OWC/TOOLKITMHD/
You will want a USB 3.0 external enclosure into which you will place the sick drive.
$22 USB 3.0 enclosure: http://eshop.macsales.com/item/OWC/ES2.5BU3W/
Purchase a 2 TB, USB 3.0 external drive as your Time Machine backup drive. Any brand will do as long as it is not WD. ( ~$100)
For example: http://www.amazon.com/Seagate-Expansion-Desktop-External-STBV2000100/dp/B00834SJ S0
See the disk replacement tutorials at macsales.com, Crucial.com, or ifixit.com.
When you open the Mac take note of which screws go in which holes. They are not all alike.
With the new drive installed, it will boot in Internet Recovery Mode when you start it in Recovery Mode (Boot, Command-R). http://www.apple.com/osx/recovery/
To force it into Internet Recovery Mode use Boot, Command-Option-R.
Use Disk Utility to partition the drive with a GUID partition and Mac OS Extended Journaled format. Then install OS X.
If you need more detailed instructions post back.
Once it is up and running place the old drive in the external enclosure and see which files you can recover.
Then setup your Time Machine backup.
Time Machine Basics: http://support.apple.com/kb/ht1427
Most commonly used backup methods:
https://discussions.apple.com/docs/DOC-3045