System: Ubuntu 14.04, Intel i7, 16GB RAM, GTX 980 video card (usually I run the 352 driver from Nvidia)
So, admittedly I am not very good at Linux. I updated to 3.19.0-65, which (as noted elsewhere) now requires Secure Boot. Nvidia drivers don't work with that, so I wasn't able to log in to the GUI on reboot. I was able to get the system to boot from the GRUB menu to the older 3.19.0-64 kernel in recovery mode, so I tried to purge the 3.19.0-65 kernel in hopes that 3.19.0-64 would become the new default. When I rebooted it was still expecting 3.19.0-65 and the boot failed.
So... cut to several hours later, and I've managed to use boot-repair-disk to fix GRUB and I can boot to the login screen again. I've purged all of the kernels, and installed only two: 3.19.0-64-generic and 3.19.0-64-lowlatency. I've also turned off Secure Boot in both GRUB (deselecting that option in boot-repair-disk) and in my BIOS.
I still can't get into the GUI - it shows the login screen at low resolution but when I put my password in it just kicks me right back to the same screen. Using ubuntu-drivers I can see my video card is "UNCLAIMED" and that doesn't change when I install the driver from a terminal and/or reboot. And that's only in the "lowlatency" kernel - in the "generic" kernel, it takes me to the screen where I enter the passphrase to decrypt my harddrive, and the keyboard doesn't work (no characters appear no matter what I type).
I'm really at a loss here, please let me know what additional information I can provide.