Crash after update to 11.10, from 11.04

It looks like your computer has more or less finished booting, but there's no display.

Likely solution

Try hitting Ctl-Alt-F2 (or Ctl-Alt-Fn-F2 if your keyboard has media keys). Do you get a login prompt? If so, enter your username and password, plug in an ethernet cable if possible, then enter the following command:

sudo apt-get update && sudo apt-get upgrade

Chances are this command will fail, and recommend a command to fix broken packages. Try that command, and then reboot with

sudo shutdown -r now

Possible solution

Hold Shift after turning your computer on. You'll be presented a program called GRUB that lets you select and boot different, older OS kernels. Try a few; maybe one will work.

Another Possible Solution

sudo apt-get install lightdm-gtk-greeter

note: it took a while for the desktop to load once I got passed the login screen.

Last resort

Boot into a live environment (that is, use an Ubuntu LiveCD or LiveUSB) and open the file browser. Mount your hard drive ('File System' in the left pane), and backup all important files onto physicial media or the internet.

Then install for a fresh system.

[NOTE: I'd probably wait a while before moving on to The Last Resort. A grizzled UNIX graybeard may come along with a more palatable solution]