Use the dpkg tool to force the removal of some kernel packages. This is not suggested for common use and is a bit dangerous, but in such case with unmet dependencies might help.
First of all, locate the kernel in which the system is booted. The one that is currently loaded. Open a terminal (CTRL+ALT+T) and issue the following command
uname -r
It will show you the loaded kernel; you should NOT try to remove this one.
Then issue the command
ls /boot
It will return all the installed images. Pick one or two and try to remove them. Try to force remove/purge them. For example
sudo dpkg --force-all -P linux-image-3.13.0-32-generic
You can do the same for other images, to free up some space.
Then you can try to install the missing packages, or
sudo apt-get install -f
to try to resolve the dependencies.
Finally, issue the “clean up old kernels” command
sudo apt-get purge $(dpkg -l linux-{image,headers}-"[0-9]*" | awk '/ii/{print $2}' | grep -ve "$(uname -r | sed -r 's/-[a-z]+//')")
Above command will remove ALL the kernels except the one that is currently loaded.
Because you have a separate /boot partition, keep in mind you will need to track its space and cleaning up often (the frequency depends on the space of /boot)
Original Source: http://askubuntu.com/questions/585736/cant-clean-a-full-boot-because-of-unmet-dependencies