Internal HD won't mount in Recovery Mode

What version of OS X was pre-installed when it was new? If you plan on giving it away, then you need to erase the drive and install the version that csme with the computer. if it was on DVD, then you need the installer discs.

Before Selling or Giving Away Your Pre-Lion Mac

Follow these instructions until you get to Step 5:

What to do before selling or giving away your Mac - Apple Support

When you reach Step 5 you will need your Snow Leopard or earlier installer disc that came with the computer when it was new.

Follow these steps for installing the original version of OS that came with the computer.

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 see

a 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 completed quit DU and return to the installer. 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.

Otherwise, if it came with Lion or later:

What to do before selling or giving away your Mac - Apple Support

There is something wrong with your boot volume. If the volume is grayed out it can still be selected to either mount or erase or even try to repair.

Did you not state that you planned to give the computer away? If so, then wiping it is something you must do in order for the next owner to configure it as theirs. I can't tell you much more without more information. It would help to see a screen shot of Disk Utility's window.

To post screen shot do this:

1. Press COMMAND-SHIFT-4 which will change the cursor to crosshairs.
2. Hold down the mouse button and use the crosshairs to select the part of the screen you wish to capture.
3. Release the button and the image will be saved to your Desktop.
4. Click on the Camera icon in the toolbar of the forum message editor.
5. Drag the image onto the Choose File button and click on the Insert button.

Does your drive have a Desktop icon that's visible? Have you tried using the Mount button in the toolbar? You will need to start from your Recovery HD or a bootable external drive first. Since you can boot from the volume it must be working with everything intact. And, you can boot from the Recovery HD. If you cannot mount the drive from Disk Utility, then open the Terminal in the Utilities folder. At the prompt enter:

sudo diskutil mount /dev/disk0s2

Press RETURN. Enter your admin password when prompted. It will not echo into the Terminal window. Does it work? If it doesn't snap a picture of the Terminal window and post it in your reply.

Yes, that is the case. Never use FileVault, so I don't think I can help beyond this. You could disable FileVault, then see what happens. But that will take a while.