I had a specific problem and it took some time to solve. I thought I'd detail it as best I could. I'm somewhat of a linux newbie.

I had ubuntu 13.11 on a Lenovo T430 Thinkpad. It has full disk encryption. Any time I boot it up, I have to type in a long key before I can even reach the log in screen. This is pretty cool.

I was using KDE. KDE had a notification which suggested I upgrade to the latest version of ubuntu (14.04). Using the gui tools that KDE presented to me, I upgraded, and rebooted. Things are working okay at this point.

I try to launch eclipse and get a problem with java. Eclipse crashes during the launch. I notice during this that KDE has given me a notification about the driver for my Nvidia GF108M. I click and I note there are 5 options for the driver. 2 new binary drivers - 1x proprietary, 1x proprietary + tested. 2 legacy binary drivers. 1 open source x.org x-server driver. Currently the open source one is selected. I select the proprietary, tested driver "Nvidia binary driver- version 331.38 from nvidia-331 (proprietary, tested)". I reboot.

When the computer comes back up, it comes back up with a blank screen. I saw the splash screen with "Lenovo" on it (bootloader, maybe?) and then the screen hung out being black. I took some steps to try to solve the problem.

1) I tried booting from a USB drive that had ubuntu on it. This worked fine.
2) I tried booting into recovery mode from the ubuntu on my computer. I would go to the grub menu and select "advanced options for ubuntu" instead of ubuntu, then select 13.11 recovery mode. This would display some stuff as it tried to boot, then hang on "loading initial ramdisk".
3) google tells me that this usually means I need to add "nomodeset" to the list of things in the grub. So I try that and try launching with a nomodeset grub. I try doing it temporarily, and I also try messing around with grub by booting from the usb drive and using chroot.
using nomodeset doesn't seem to actually work.
4) I spend a long time alternating between it being a graphics driver problem (since that's the last thing I messed with) and it being a problem where for some reason grub can't recognize that the volume is encrypted.
5) eventually I figure that if it's a graphics problem, maybe I'm actually at the screen where you put in your encryption key when it says "loading initial ramdisk", it's just having trouble displaying it. I type in my encryption key and hit enter, and the computer boots up normally.