Here's the situation: I have a separate /home partition to make installs and upgrades easy. I just installed the latest version of Ubuntu 14.04. Everything was great. I installed the LXDE desktop (not Lubuntu) via synaptic. Everything works fine. I could boot into the Unity desktop and the LXDE desktop.
Then I installed KDE desktop via synaptic. The boot splash changed, which is fine, but now I can only boot into KDE or LDXE. If I try to boot into Unity, I'm stuck at the splash screen. If I push the power button, the splash goes away, and I see the tail end of a shut-down, as if I'd executed
sudo shutdown -h now in a terminal.
I could simply reinstall, and never use KDE, but I like that option from time to time.
I found the problem. KDE switched the default display manager to KDM which didn't want to play with Unity. All I needed to do was switch back to lightdm using
sudo dpkg-reconfigure lightdm
as suggested in this question/answer.