Using Ubuntu 12.04 and recently go the message about Hardware Enablement Stack (HWE) EOL and to update with apt-get install linux-generic-lts-trusty linux-image-generic-lts-trusty
All nice and good, the update went without any problems and did a reboot.
The machine did not start again.
The problem is that the machine is located in a DC...pretty far away.
I had to go to the DC and troubleshoot the machine.
It seems running the above command messed up grub.
I needed to boot a Live Distro and do a grub-install /dev/sda which fixed my problem.
Take good care when you update HWE, specially if you do not have physical access to the machine.