The following answer was provided by user239585 (the question asker):
Your disk will likely be read-only in recovery mode. Run this command to make it not so:
mount -o rw,remount /
The problem is that during your upgrade, some of the packages did not download/install correctly. To correct this problem, you will need to run a series of commands. If you are on a wired connection, however, you will first need to run:
vi /etc/network/interfaces
Add the following two lines:
auto eth0 iface
iface eth0 inet dhcp
Save (command mode, zz)
Then run this command:
sudo /etc/init.d/networking restart
Now run the following commands in succession, being that you are connected to the internet and your disk is writable:
sudo dpkg --configure -a
sudo apt-get update
sudo apt-get install -f
sudo apt-get upgrade
sudo apt-get dist-upgrade
sudo dpkg --configure -a
Then, as you guessed, just type:
reboot
And all should be well. You may still get the recovery screen on your next boot, but just select the top option, Ubuntu. When the cursor appears, you know you're good, because that is a sign that X server is running properly. After following these instructions, I have 13.04 with XFCE and all important files in tact.