Screen stuck at the Ubuntu logo

Check your file system for errors.

To check the file system on your Ubuntu partition...

• boot to the GRUB menu
• choose Advanced Options
• choose Recovery mode
• choose Root access
• at the # prompt, type sudo fsck -f /
• repeat the fsck command if there were errors
• type reboot

If for some reason you can't do the above...

• boot to a Ubuntu Live DVD/USB
• start gparted and determine which /dev/sdaX is your Ubuntu EXT4 partition
• quit gparted
• open a terminal window
• type sudo fsck -f /dev/sdaX # replacing X with the number you found earlier
• repeat the fsck command if there were errors
• type reboot

Update #1:

The fsck found and fixed errors on your file system, but the system continues to not boot fully. Other file corruption is possible. Booting to an older kernel works fine.

If you wish to continue to try troubleshooting the non-booting kernel, follow the procedure shown below, otherwise boot to the newest booting kernel, backup your files, and reinstall Ubuntu, then do Software Updates.

• use the first method from my original instructions and boot to the newest kernel (that doesn't fully boot), and get to the # prompt.
• type sudo pico /etc/default/grub and use the arrows keys to navigate to the line that contains "quiet splash" and delete the words quiet and splash so that you're left with "". Remember this line, as you'll need to reinsert those words back later, once the machine boots properly.
• control-o # to save the edit
• control-x # to exit the editor
• sudo update-grub # to update grub
• reboot # to reboot the computer

The machine still won't fully boot, but it'll show you on the screen where it's stopping, along with any error messages. Report back. Edit your original question with any important details, and then send me a comment that starts with @heynnema to alert me.