Today I had a very similar problem — after updating the system, rebooting and logging in, only the blue screen appeared without any signs of Unity. The way I fixed it was this.
Switched to tty1 (Ctrl+Alt+F1), logged in and made sure that all updates have been applied (sudo apt-get update && sudo apt-get upgrade).
Installed gdm by executing sudo apt-get install gdm. This automatically invoked configuration where I have selected gdm instead of lightdm. Installation of gdm lead to uninstallation of unity.
Rebooted, switched to tty1, logged in, and installed unity by executing sudo apt-get install unity and then ran sudo dpkg-reconfigure gdm where I have selected lightdm this time.
Rebooted, logged in using the graphical prompt and Unity loaded as hoped for.