Kernel downgrade after update broke my system
You can remove the non-functional kernel with apt-get:
sudo apt-get purge linux-image-3.8.0-33-generic
As part of uninstallation process the system removes 3.8.0-33 entry from GRUB menu and leaves only 3.8.0-29.
Please note, that also package linux-image-generic-lts-raring will be removed. That means that your kernel version will not be upgraded in future with apt-get upgrade. Only when you reinstall linux-image-generic-lts-raring will the kernel version get upgraded. So this is a permanent solution.