How to resume or abandon an apt-get dist-upgrade after connection reset?
You can kill apt-get and simply run it again after running dpkg --configure --pending to configure previously already installed packages.
If you are unable to continue because the system is broken, you could try to fix it with apt-get:
apt-get --fix-broken install
See a similar question over at Unix & Linux, https://unix.stackexchange.com/questions/46534/how-to-safely-resume-an-aptitude-dist-upgrade-after-ssh-timeout.