Upgrade from 14.04 to 16.04 fails (with video)

https://youtu.be/0pHVeeHbE9I

After ruing the command "do-release-upgrade", the upgrade process seemed to complete. I did notice some errors, such as this message that appeared multiple times:

GLIBCXX_3.4.21 not defined in file libstdc++.so.6 with link time reference

Anyways, after the installation process told me it was finished, and rebooted, all I get is a endless cycle of an error message appearing for a fraction of a second, and then what appears to be a flash in the screen then a reboot or something. I can't enter the grub menu by pressing shift while on the boot logo screen. I tried multiple times, the menu won't come up. What can do to fix this situation without wiping the drive clean?