How to boot the new kernel in Ubuntu?

I have a droplet that was created when ubuntu 12.04.4 was the most current. Unfortunately, 12.04.4 is no longer a supported HWE stack. I updated:

apt-get -y update && apt-get -y upgrade && apt-get dist-upgrade && shutdown -r now

After reboot, it says

Your current Hardware Enablement Stack (HWE) is no longer supported
since 2014-08-07.  Security updates for critical parts (kernel
and graphics stack) of your system are no longer available.

For more information, please see:
http://wiki.ubuntu.com/1204_HWE_EOL

To upgrade to a supported (or longer supported) configuration:

* Upgrade from Ubuntu 12.04 LTS to Ubuntu 14.04 LTS by running:
sudo do-release-upgrade 

OR

* Install a newer HWE version by running:
sudo apt-get install linux-generic-lts-trusty linux-image-generic-lts-trusty

So I ran the install

apt-get install linux-generic-lts-trusty linux-image-generic-lts-trusty

But after reboot, it’s still running kernel 3.8.0-29-generic

# uname -a
Linux hostname 3.8.0-29-generic #42~precise1-Ubuntu SMP Wed Aug 14 16:19:23 UTC 2013 x86_64 x86_64 x86_64 GNU/Linux

I looked into grub … Read through /etc/default/grub and /boot/grub/grub.cfg and confirmed everything there looks like it makes sense. Default entry is 0, and first entry in cfg file is 3.13.0-39. Ran the following anyway, and confirmed the files still look like they make sense…

grub-set-default "Ubuntu, with Linux 3.8.0-29-generic"
grub-reboot 'Ubuntu, with Linux 3.13.0-39-generic'
update-grub
shutdown -r now

Still it comes up with 3.8.0-29-generic. I watch the console, and it doesn’t even try 3.13.0-39. Which makes me think, maybe digitalocean isn’t using grub or something?