That /boot partitions was probably created and made too small automatically. The installer creates a /boot partition when you opt for an encrypted hard drive.
to get rid of old kernel images. If it complains that it can't, because you have to fix the package manager first, run these two commands
sudo apt-get autoremove
They should give you the presently running kernel and a list of installed kernel packages. Uninstall the kernel packages older than your running kernel with
dpkg --list | grep linux-image
You write you can't install 14.04 because of this problem. But you can surely do a clean install, you just can't upgrade. If you do a clean install, keep all files backed up on an external drive. It is possible to keep your home directory during reinstallation, but don't count on it, especially not on encrypted systems.
dpkg -P linux-image-<version>