Teste isso:
Você deve inicializar a partir de um live-dvd / usb.
Abra um terminal.
Execute:
sudo -i
fsck -a -t ext4 /dev/sda5
mount /dev/sda5 /mnt
mount --bind /dev /mnt/dev
mount --bind /dev/pts /mnt/dev/pts
mount --bind /proc /mnt/proc
mount --bind /sys /mnt/sys
chroot /mnt
grub-install --root-directory=/mnt /dev/sda
update-grub
umount /mnt
reboot