Set the boot files and boot the system from the GRUB prompt.

This blog post is sourced from the following web site 
https://www.linuxfoundation.org/blog/blog/classic-sysadmin-how-to-rescue-a-non-booting-grub-2-on-linux

When you’re at the grub> prompt, you have a lot of functionality similar to any command shell such as history and tab-completion.

Use the ls command to list the contents of various partitions 

and identify the linux root partition

grub> ls

The boot/ folder in the root partition would contain the linux

kernel and intrd image (initial ramdisk image)

Set the root partition, kernel and intrd image using grub> prompt
grub> set root=(hd0,gpt2)
grub> linux /boot/vmlinuz-3.13.0-29-generic root=/dev/sda2
grub> initrd /boot/initrd.img-3.13.0-29-generic
grub> boot

The first line sets the partition that the root filesystem is on. The second line tells GRUB the location of the kernel you want to use. Start typing /boot/vmli, and then use tab-completion to fill in the rest. Type root=/dev/sdX to set the location of the root filesystem. Yes, this seems redundant, but if you leave this out you’ll get a kernel panic. How do you know the correct partition? hd0,1 = /dev/sda1. hd1,1 = /dev/sdb1. hd3,2 = /dev/sdd2. I think you can extrapolate the rest.
The third line sets the initrd file, which must be the same version number as the kernel.
The fourth line boots your system.
When you have successfully booted your system, run these commands to fix GRUB permanently:
 sudo update-grub
 sudo grub-install /dev/sda