At the Grub boot menu you can select Advanced options for Ubuntu and then select recovery mode. At the recovery menu you can then select Resume. If that gets you to a working desktop go to System Settings>Software & Updates>Additional Drivers tab and select another video driver. Start with the open source video drive and once you have a working desktop with the open source video driver you can experiment with that.
Newer versions of Ubuntu come with newer versions of proprietary video drivers which do drop support for older video adapters. I think it is always best when upgrading to a newer version of Ubuntu to revert to using the open source video driver. You may not have done that.
Also, from the Advanced options>Recovery mode we can select Root and get to a root shell prompt. There we can update the system. which may finish the upgrade if it has not finished.
When finished, press Enter to get back to the recovery menu.