How to recover a compromised Mac OS 10.8.5
If you are having issues during installation of OS, run Disk Utility from the Install DVD and see if there are any issue reported from checking the disk.

If you have a backup of all your files on an external drive already and are comfortable with erasing your internal drive then you might have to erase and install the OS from the DVD.

Booting with alt will give you a listing of all bootable volumes your Mac has including the main hard drive partition (10.8.5), optionally it can show the Recovery HD, and with the install DVD inserted you will see that as well.

If you see the Recover HD then select that and proceed with OS install. If it doesn't show up then use the DVD as your best tool.