"ALERT! /dev/mapper/ubuntu--vg-root does not exist "
Solution 1:
I had the same problem on a Dell XPS-13 soon after a fresh Ubuntu 16.06 install, but was unable to successfully 'exit' BusyBox.
I powered the laptop on while holding ctrl, selected System Settings from the boot menu, entered 'SATA settings' and changed from RAID to AHCI
Apparently RAID harddrives aren't supported by Ubuntu
This immediately solved the problem for me