Inicia el modo rescate desde un live CD y saca el log /var/log/kern.log
 Puedes probar esto:
add-apt-repository ppa:yannubuntu/boot-repair
sudo sed 's/trusty/saucy/g' -i /etc/apt/sources.list.d/yannubuntu-boot-repair-trusty.list
sudo apt-get update
sudo apt-get install -y boot-repair && (boot-repair &)
after that, boot-repair should open automatically

click the "advanced options" to expand
in the "Main options" tab, check "Reinstall GRUB" and "Repair file systems" Repairing file systems is the most important part as the kernel panics happen because of some file system error.
int the "Grub options" tab, check "Purge GRUB before reinstalling it"
and of course you must have internet connection as you will be installing new files. and finally click Apply.