It looks like some parts of your
/boot directory may have been already damaged when the backup was taken. Do you have an older backup you could try restoring?
Alternatively, you could try booting the system to rescue mode from a CentOS 5.9 installation media: it will ask you to select the language and keyboard layout just like in the beginning of a regular installation, then switch into rescue mode: it will allow you to activate a network interface and then (hopefully) automatically mount your installed system to
/mnt/sysimage. Then it will give you a root shell, with a suggestion that the command
chroot /mnt/sysimage will allow you to access your installed system.
So use the suggested command, and then check the integrity of the kernel packages:
rpm -V 'kernel-PAE*'
If the kernel package is OK, the
rpm -V command will display nothing.
If the kernel package is damaged, you might try to reinstall it with
yum reinstall kernel-PAE or similar command.
If you haven't already configured this system to use the archive repositories at vault.centos.org, you might have to do that first. As the GPG keys of CentOS 5.x have probably expired by now, you might have to set
gpgcheck=0 in the repository configuration for it to allow the packages to be installed.
To reinstall GRUB on your system disk, first run
cat /boot/grub/device.map and verify it makes sense regarding your current system configuration (i.e.
(hd0) is referring to the disk that will be your system disk when your system is running normally) and adjust if necessary, then run
grub-install /dev/sda, replacing
/dev/sda with your actual system disk device.
exit twice: the first
exit will undo the
chroot /mnt/sysimage command, and the second will exit the rescue environment, which will trigger an automatic reboot.