This link shows you how to boot into recovery mode. Use root with networking enabled.
Run this code to remount your hard drive with read-write privileges.
mount -o remount,rw /
Then remove your nvidia drivers. Someone has already made a great guide on that, here on the site.
How can I uninstall a nvidia driver completely ?
It should work for Ubuntu 13.04 as well, I use the same thing.
By the way, Nvidia drivers are just a pain. If you can survive with the neuveau drivers, use them. Otherwise, I suggest you get your computer fully updated from the PPAs, do a full shut down and boot, install the Nvidia drivers again, (or try another driver) and do another full reboot. If it works great, if not try again all over from your black screen problem. This I found is the best way to get it working, and I did get my GTX570 HD working beautifully, and I can even update the driver every time a new version comes out and they usually all work, no matter what driver I install now.