Trying to start a computer with Ubuntu 16.04 LTS leads to the following error message

 Kernel panic - not syncing: VFS: Unable to mount root fs on unknown-block(0,0)

and the computer will not boot into the OS.

The problem is, that the initramfs is a defect due to update processes of the linux kernel.

By googleing you can find this error message and possible solutions quite often and I just want to summarize their and my experiences.

A good solution is to boot your computer with a Ubuntu Live from an USB stick or DVD. Just follow the instructions on the Ubuntu homepage how to create such an USB stick (or DVD). After booting in your rescue system, open a terminal and identify the harddisk with your systems is on.

sudo fdisk -l

Mount this harddisk (e.g. /dev/sda1) and the devices from your host rescue system to create a chroot environemnt.

sudo mount /dev/sdax /mnt
sudo mount --bind /dev /mnt/dev
sudo mount --bind /dev/pts /mnt/dev/pts
sudo mount --bind /proc /mnt/proc
sudo mount --bind /sys /mnt/sys
sudo chroot /mnt 

To create a new initramfs you have to find out which kernel you want to boot. Just have a look into /boot and identify the latest one. Just type

update-initramfs -u -k 4.4.0-66-generic

with the version number you found.

When no error occurs you can finally reinstall grub by typing the following and reboot

update-grub2

In my case I got some erros due to the big number of older kernels in the /boot directory. After deleting them manually the grub update worked fine and I could manage to restart the computer.