Q: unable to boot recovery mode

That sounds like the Recovery HD is damaged. If you plan to sell it, however, here's what you need to do: What to do before selling or giving away your Mac. If your model originally came with Snow Leopard or earlier pre-installed, then you will need to do this instead:

Follow the instructions above until you get to Step 5:

You will need a Snow Leopard DVD or the OS X Installer DVD that came with the computer. Follow these steps:

1. Boot the computer using the Snow Leopard Installer Disc or the Disc 1 that came with your computer.  Insert the disc into the optical drive and restart the computer. After the chime press and hold down the  "C" key.  Release the key when you seea small spinning gear appear below the dark gray Apple logo.
2. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After Disk Utility loads select the hard drive entry from the left side list (mfgr.'s ID and drive size.)  Click on the Partition tab in the DU main window.  Set the number of partitions to one (1) from the Partitions drop down menu, click on Options button and select GUID, click on OK, then set the format type to MacOS Extended (Journaled), then click on the Apply button.
3. When the formatting has finished quit Disk Utility.  Proceed with the OS X installation and follow the directions included with the installer.
4. If you are planning to sell or give your computer away, then do the following: After you reformat your hard drive and reinstall OS X, the computer restarts to a Welcome screen and asks you to choose a country or region. If you want to leave the Mac in an out-of-box state, don't continue with the setup of your system. Instead, press Command-Q to shut down the Mac. When the new owner turns on the Mac, the Setup Assistant will guide them through the setup process.

[Permission to use part or all of the above has been granted by Kappy, exclusively, to theratter.]