MacOS – Horizontal line appears in fullscreen mode

The error message "Mac OS X Lion couldn't be install, because the disk Macintosh HD is damaged and can't be repaired." in the photo above would indicate that there is either a problem with the physical hard drive of your Mac or the Mac's "Macintosh HD" volume is damaged at a software level.

While you're in the installer you can click on Window > Installer Log to view a log from the Lion installer. This may give you some clues as to what is causing the error. For instance, any mention of "Disk I/O Error" would be an indicator that there is a communication problem with the hard drive at a hardware level.

You can also attempt to repair the Macintosh HD volume using Disk Utility (should be accessible from the Lion installer's Utility menu), or reformat it again if the repair fails. Once repaired or reformatted you can attempt the installation again.

Hopefully that helps.

You know the answer already.

For some reason your booth sector got scrambled.

You could try to the reset EFI to see if it helps.

An EFI (extensible firmware interface) is a set of instructions stored in computer memory that act as an interface between computer components and the operating system during startup. If you are having startup problems or your computer components do not work properly, you may be able to solve the problem by resetting the EFI to its default settings.

Read more : http://www.ehow.com/how_8007618_reset-efi-chip.html

Reinstalling the OS with CMD-R will only fix the system files and not your files. It depends if you have the Restore on your hard drive or you need to use the Internet recovery.