Cannot update kernel Ubuntu 16.04

Question

I'm trying to update the kernel on a VPS to 4.8 (or 4.8.X), but for whatever reason it's ignoring grub or something else is happening.

uname -a produces Linux vlanp 2.6.32-042stab120.6 #1 SMP Thu Oct 27 16:59:03 MSK 2016 x86_64 x86_64 x86_64 GNU/Linux

I followed the instructions on the following page: http://linuxg.net/install-kernel-4-8-on-ubuntu/ and running the command dpkg --list | grep linux-image lists it as installed:

ii  linux-image-4.6.0-040600-generic           4.6.0-040600.201606100558                     amd64        Linux kernel image for version 4.6.0 on 64 bit x86 SMP
ii  linux-image-4.6.0-040600-lowlatency        4.6.0-040600.201606100558                     amd64        Linux kernel image for version 4.6.0 on 64 bit x86 SMP
ii  linux-image-4.8.0-040800-generic           4.8.0-040800.201610022031                     amd64        Linux kernel image for version 4.8.0 on 64 bit x86 SMP
rc  linux-image-4.8.10-040810-generic          4.8.10-040810.201611210531                    amd64        Linux kernel image for version 4.8.10 on 64 bit x86 SMP

I have attempted to reboot using grub-reboot <number> to try and get the kernel to boot at least once, but it reboots into 2.6 every time.

• There is no /etc/default/grub file
• There is no /boot/grub/grub.cfg file

Here's the kernel list from /boot/grub/menu.lst:

title           Ubuntu 16.04.1 LTS, kernel 4.8.0-040800-generic
root            (hd0,0)
kernel          /boot/vmlinuz-4.8.0-040800-generic root=/dev/hda1 ro quiet splash
initrd          /boot/initrd.img-4.8.0-040800-generic

title           Ubuntu 16.04.1 LTS, kernel 4.8.0-040800-generic (recovery mode)
root            (hd0,0)
kernel          /boot/vmlinuz-4.8.0-040800-generic root=/dev/hda1 ro  single
initrd          /boot/initrd.img-4.8.0-040800-generic

title           Ubuntu 16.04.1 LTS, kernel 4.6.0-040600-lowlatency
root            (hd0,0)
kernel          /boot/vmlinuz-4.6.0-040600-lowlatency root=/dev/hda1 ro quiet splash
initrd          /boot/initrd.img-4.6.0-040600-lowlatency

title           Ubuntu 16.04.1 LTS, kernel 4.6.0-040600-lowlatency (recovery mode)
root            (hd0,0)
kernel          /boot/vmlinuz-4.6.0-040600-lowlatency root=/dev/hda1 ro  single
initrd          /boot/initrd.img-4.6.0-040600-lowlatency

title           Ubuntu 16.04.1 LTS, kernel 4.6.0-040600-generic
root            (hd0,0)
kernel          /boot/vmlinuz-4.6.0-040600-generic root=/dev/hda1 ro quiet splash
initrd          /boot/initrd.img-4.6.0-040600-generic

title           Ubuntu 16.04.1 LTS, kernel 4.6.0-040600-generic (recovery mode)
root            (hd0,0)
kernel          /boot/vmlinuz-4.6.0-040600-generic root=/dev/hda1 ro  single
initrd          /boot/initrd.img-4.6.0-040600-generic

title           Ubuntu 16.04.1 LTS, memtest86+
root            (hd0,0)
kernel          /boot/memtest86+.bin