Ubuntu – Grub Doesn’t Load after Update

1. Use a Windows Recovery disk this way: https://help.ubuntu.com/community/RestoreUbuntu/XP/Vista/7Bootloader , until you get direct access to Windows.
2. Then run Boot-Repair to recover the GRUB menu.

First off a few words on UEFI/BIOS boot device selection versus a boot loader (e.g. grub) for selecting an OS to be booted:

Any hard drive has a master boot record at the beginning of the drive. In this area the information on how to start the boot loader of this drive is stored (e.g. where to find it, what to do). The boot loader then can see the different operating systems of the hard drive and the partitioning scheme. The BIOS selection is only to define which medium to boot from - and this means which medium to use for reading said master boot record. The medium could be an optical disk (drive), a flash drive or a (physical!) hard disk. It does not know about anything written on this disk and thus cannot see any partitioning. However you may e.g. choose if you want to boot from your SSD or your HDD.

Now for the solution of your problem:

As explained above, you always need a boot loader on a hard drive with different OSs (and the respective partitions). This is the very thing missing in your installation. The Ubuntu you installed is fine, but it cannot be found, the Windows boot loader that is still active won't display it (complain to MS for that matter).

So all we need to do is install grub.

For this boot from your Ubuntu installation CD and select a live version ("try Ubuntu"). If the live version doesn't already have boot-repair available (I think it is included by now), install it by opening a terminal and typing:

sudo add-apt-repository ppa:yannubuntu/boot-repair
sudo apt-get update
sudo apt-get install boot-repair

Start the program and follow the instructions.