I have just updated to 13.10. The system boots and loads, and the GUI login screen appears. After logging in, however, I am left with the colorful splash screen and nothing else happens. I can use ctl-alt-F1 to get to a terminal login, but I don't know how to analyze this problem or to converge on a solution. Together with the Ubuntu upgrade, I installed a graphics card...Radeon R7 260X. According to the AMD site, there is a Linux driver for this card, but I don't know how to install it, and I don't even know if that is the problem. Any help would be much appreciated.
You should try logging in a terminal session (Ctrl+Alt+F1 to get to it) and read the content of /var/log/Xorg.0.log to get some more clue regarding your problem.
Also, once you get to the terminal session install the package jockey-common and then run