14.04 - Can't boot after apt-get update && upgrade

I'm running 14.04. I ran sudo apt-get update and sudo apt-get upgrade, which failed with an error:

dpkg: error processing archive /var/cache/apt/archives/
    linux-image-3.19.0-66-generic_3.19.0-66.74~14.04.1_amd64.deb (--unpack):
    cannot copy extracted data for './boot/System.map-3.19.0-66-generic'
    to /boot/System.map-3.19.0-66-generic.dpkg-new':
    failed to write (No space left on device)

Now, my machine won't boot. I can get to the login screen, but when I enter my password, I immediately get logged out after seeing a glitchy screen like this (sorry for the glare):

Trying to boot in recovery mode gives me this output:

(mountall: fsck /boot [957] terminated with status 1)

It looks like there's a problem with /boot, but I can't figure out how to repair it.

I've also had trouble booting from more recent kernels, so I've been booting from 3.19.0-49.

With the help of Byte Commander's comments, I was able to fix this using these steps:

• Open a root shell in recovery mode


• Make the filesystem writable: mount -o remount,rw /


• Mount the boot partition: mount /dev/sda1 /boot


• Configure a network connection: dhclient eth0


• Remove unused kernels; this took some improvising, but it was mainly a combination of apt-get purge linux-image-x.x.x-x, dpkg --force-all -P linux-image-x.x.x-x-xxxxxx, and apt-get install -f.

tl;dr: don't let your boot partition get full.